The larger a government gets, the more bureaucracy it accretes, the easier for things to slip between the cracks, the harder for things to get done.
And that's on Earth. Imagine a galaxy full of inhabited planets, with billions of people on each one, and probably not a Planet of Hats. Even an FTL drive and form of communication would not decrease the disadvantages of scale. Without the communication, difficulties would be increased — massively so if only STL travel is possible.
Worse yet, mix in aliens with their alien thought paths — but it would be impossible even with a wholy human galaxy, or a substantial portion of it, or even a solar system well filled up with inhabitable locations.
Sci-Fi Writers Have No Sense of Scale, but sometimes, they realize that human government can not reach that far.
Comes up when a Galactic Superpower fails to govern.
This may lead to An Aesop about Pride and how man's reach exceeds his grasp in trying to control such a massive space. Often the cause of Vestigial Empire...IN SPACE!
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Serenity mentions offhand that despite the Anglo-Sino Alliance having jurisdiction over the entire star system in which the Firefly franchise takes place, they don't have the manpower to provide effective security everywhere. On a lot of the more sparsely populated planets and moons they contract out to private companies.
In Poul Anderson's "Starfog" Laure explains that they are too large and disorganized to provide assistance to the spaceship. True, they have the money, here and there, but they do not have the focus to gather it up.
In Michael Flynn's Spiral Arm series, two sections of the galaxy are nominally controlled. It is observed that the Ardry's authority really runs to wherever his Hounds are operating and no farther. In On The Razor's Edge, a character makes a point that the Ouroborus Circle means that the Ardry has more control.
In the Worlds of Shadow series, the Galactic Empire has telepathic mutants for communication, but outback worlds, such as the asteroid that the protagonists land on, can pretty much do what they like including keeping slaves, since it takes months to get anywhere by ship.
In the Honorverse the exodus from Earth lead to the creation of several star nations, most prominently Manticore and Haven. The oldest and largest is the Solarian League, which eventually becomes so large and bureaucratic that it begins to collapse under its own weight.
In Mikhail Akhmanov and Christopher Nicholas Gilmore's novel Captain French, or the Quest for Paradise, the same trope applies but with Absent Aliens and lack Casual Interstellar Travel. Over 20,000 years of space exploration, humanity has colonized dozens of worlds, but the lack of FTL travel means that only a hundred or so ships regularly travel between them. The only way to travel between stars is to use a near-light STL drive that instantaneously accelerates to relativistic speeds, meaning the journey takes only a second to the traveler but can take decades or even centuries for the rest of the universe. Under these conditions, and with no Subspace Ansible to facilitate communication between worlds, each world is on its own. The authors explain that no interstellar government is possible, as a rebellion on one world could not be put down by a Space Navy because it would take years for the ships to arrive. Even sending signals across interstellar space is a costly venture without any benefit. The only real means of spreading news between worlds is via the space traders.
Averted in Harry Harrison's To the Stars trilogy, where the dictatorial Earth government (minus several "rogue" nations such as Israel, the last democratic state) has a number of colonies on other worlds. In order to avoid insurrections, they are deliberately kept dependent on something that only Earth can provide. Usually, this means Crippling Overspecialization in colonies. Even after La Résistance manages to win, it's clear that something will need to be done about the colonies in order to make them more self-sufficient in order to prevent this from happening again.
In Harry Turtledove's Homeward Bound, after humans prove that FTL Travel is possible, Fleetlord Atvar suggests to the 37th Emperor Risson (Emperor Risson XXXVII using the human naming system) that colonization of hundreds of worlds is necessary in order to keep the Empire from being vulnerable to humans. Since the Empire now consists of 3.5 worlds (Home, Rabotev 2, Halless 1, and half of Earth), Mutually Assured Destruction is a real possibility. In response, Risson replies that there is no way the Empire would stay together under these conditions, even accounting for FTL travel. Atvar agrees but claims that the Race will survive.
In Andrey Livadny's The History of the Galaxy books, the Confederacy of Suns is created in the aftermath of the First Galactic War to provide mutual defense and trade of the victorious Free Colonies. From the beginning, the set-up is not equal, as the five Core worlds have more power than the worlds making up the far larger Periphery. While the Confederacy lasts for a surprisingly long time, after about 1000 years, the internal strife and the desire for self-control of many worlds (not to mention corruption) results in the break-up of the Confederacy. Only a crippling attack by a previously-unknown alien race decades later bands the now-separate worlds together, re-forming the Confederacy on new terms (i.e. equality for all worlds, including a few alien ones).
Downplayed in the Star Wars Expanded Universe. Though the Republic (and then the Empire, and then the Republic again) lay claim to the vast majority of (known, inhabited) galaxy, keeping it is another matter entirely. The New Republic was especially prone to nearly coming apart at the seams, only to be united by a new, greater threat (usually the Empire, which both sides were prone to pointing out). The Empire kept somewhat better control of its territory, at the cost of vastly increased military expenditure and curtailed rights (and we all know how that ended).
In A Deepness in the Sky, there is no Faster-Than-Light Travel or FTL communication, so solar systems are effectively isolated. Coupled with the extreme cost and next to zero returns from constructing the Ram Scoop interstellar spacecraft, there are only two interstellar societies - the largely fragmented Qeng Ho traders, and the Emergents (who have only been around for a short time). Most societies break down after a few hundred years from stagnation courtesy of the physics of the inner Milky Way preventing high-tech equipment like nanotechnology, faster than light travel or true artificial intelligence from working - all of which make interstellar empires possible in the A Fire Upon The Deep which is set near intergalactic space, where physics are more forgiving.
Also in the Vorkosigan Saga, FTL travel is accomplished using space-folding jumpships traversing a complex network of natural wormholes. Direct travel between star systems is limited to those that have wormhole connections between them. Some, including Earth itself, sit in cul-de-sacs in the Nexus and require travel through other systems to get to. There are no FTL communications. Instead messages are relayed to ships that carry them through the wormholes and then retransmit them to other ships traveling to the destination system. The result is that most colony worlds are independent, although a few multi-system space nations, such as the Barrayaran and Cetagandan Empires, exist. But these generally only control a handful of systems at best.
Live Action TV
Star Trek is probably one of the best examples of a governable galaxy, The Federation and all that jazz, but Star Trek: Enterprise takes place before the Federation appears leaving Earth unable to control anything outside of the Sol System with even cargo-ships ignoring the authority of Star Fleet.
the League of Non-Aligned Worlds is in theory a strict alliance bent on becoming The Federation. In actual practice, however, they are only unified by the common threat of the Centauri (even if they are ultimately overwhelmed by them. Turns out that as they shrunk, the Centauri advanced their technology enough that they can fight the whole League and win) and common commercial bonds with Earth Alliance;
the Earth Alliance is apparently unified, but the Expanded Universe makes clear that there still are independent nations on Earth itself (the Vatican for the same reasons they are still independent from Italy, and Israel with their own colony world and the Republic of Korea because they never joined the Alliance for their own reasons), even if they strongly feel Alliance pressure (Israel's independence is mostly nominal), and as Earth Alliance expanded in space two different sets of separatists slipped out and formed their own states, the Sh'lassen Triumvirate (two worlds, they join Earth Alliance during the series when the government starts losing a civil war and calls Earth for help, with joining the Alliance as condition) and the Free Human Union (three worlds, still independent).
In the Imperium of Man individual planets are normally self-governing, with taxes and men for Imperial regiments being gathered by an administration stiff and bureaucratic, operating on its own and not controlled from the top.
40K has another example with the Tau Empire, which consists of well-regulated, disciplined and highly organized planet systems where every citizen does his part without hesitation. This is possible for two reasons: the Tau operate on Happiness in Slavery where no citizen will ever try to do less than their rigidly-defined part for the Greater Good (possibly via pheromonal mind control of their ruling class), and their empire is very restrained (their form of FTL travel is something like five times slower than Warp travel, which can often take months of real-time).
The Third Imperium of Traveller can best be described as a "feudal confederation", individual planets are typically left to their own devices so long as they don't attempt to secede, withhold taxes, interfere with interstellar trade, or make war with other planets. Wars between factions on the same planet are allowed if they don't use nukes or violate any of the other rules. The Imperial Nobility primarily administrate the Imperial Ministries operating within their domains, and have hereditary posts because the Imperium is too large to advance upwards within one lifetime. And the Imperium doesn't govern anywhere near the entire galaxy, or even all of Humaniti, they're bordered by five other empires that are similarly decentralized (save for the K'kree, whose system of government was so inflexible they had to stop at 2,000 worlds).
BattleTech the Terran Hegemony and the Star League had tough times in their glory days, not only do they have to govern thousands of worlds, but they also have to hunt down pirates, and stamp out rebellion hundreds of light years away from each other. And the Successor States following the fall of the Star League have been unable to form a unified government for the past 400 years.
Halo: As humanity expanded, insurgents began to spring up on colony worlds away from the central government, prompting the UNSC to take action and eventually lead to the creation of the SPARTANs.
Mass Effect: The galaxy is, according to the Codex, barely 1% explored, let alone governed. Even among the settled worlds, there are territories that the Citadel Council has no authority over, such as the Terminus Systems, and others where there is no law at all.
Even in the regions it controls, the Systems Alliance is, well, an alliance rather than a federation; colonies can choose to opt out of the Alliance, and many do. Those who stay do so as much or more for the economic and military benefits as any particular loyalty to Earth. The Salarian Union is implied to have a similar arrangement, and the Asari Republics are even more chaotic (they are the only major species whose homeworld lacks even a de facto unified government). Only the turians exert any real control over their colonies, and they have the fewest of anyone.
Despite having much more reasonable ambitions than an entire galaxy, the United Earth Directorate of Starcraft fame finds the Koprulu Sector untameable; their fleet manages to take over the sector in a matter of weeks, but loses it just as quickly. Short reigns characterized the other Koprulu governments, with both the Terran Confederacy (less than a generation after moving from The Alliance to The Empire) and Emperor Arcturus's Dominion (roughly 4 years) falling just in the span of the games. Worse, it's contagious: neither the protoss nor the zerg had any significant change in leadership for centuries before coming to Koprulu, and neither has managed to make a leader last more than a few years since. It must be something in the space-water...
There are no less than three human governments in the Koprulu sector, the Terran Dominion, Kel-Morian Combine, and Umojan Protectorate. The latter two were conquered by the Confederacy and briefly part of the Dominion but Mengsk couldn't maintain his hold on them for long.
In the Orion's Arm galaxy, not even Sufficiently AdvancedArtificial Intelligences prove able to rule an entire galaxy. This synopsis explains some of the difficulties any space empire would likely encounter. In fact they don't rule anywhere near the entire galaxy. On this map all the Sephirotic Empires are within that fuzzy green dot (it's been only 10,500 years, and the setting does not have FTL).