A reason for the rotating directors, so each film would be stylistically unique from the other entries. Even when Christopher McQuarrie ended up being the first director to return for a sequel, he was instructed by Tom Cruise to change his direction style.
Cruise taking the initiative and doing his own stunts isnt necessary for filming but he does so anyway for the authenticity. One of the best examples is training himself to hold his breath for over six minutes to film an underwater scene in Rogue Nation. The scene wasnt filmed as a single take or anything that would actually necessitate Cruise have to do this but having the ability to do so meant the plausibility of the scene holds up because Tom can do it in real life.
Reality Subtext: The strong chemistry between Ethan Hunt and Ilsa Faust is helped considerably by the fact that Tom Cruise and Rebecca Ferguson, who play them, have a very warm and friendly relationship in real life.
Recycled Script: Both the first and third movie involve Ethan being set up by a mole in IMF who isn't revealed until near the end, and who tries to frame the boss of the organization who spends time as an Anti-Villain trying to hunt down Hunt, with the audience left unclear if its because the boss really thinks Hunt is a traitor or because the boss is the traitor. In both their actions force Ethan to go rogue and steal the MacGuffin that the bad guys are after for them, and in both The Mole is in league with an arms dealer. Each movie sees Hunt's family being dragged into the plot to get at him, sees a fairly traditional IMF plot go off without a hitch only for the team to be ambushed after the fact, and features a reference ot Ethan evading airport security despite IMF putting "a guy at the airport". In a more general sense, every film except the second has used the premise of Ethan being forced go on the run from his own government.
Sequel Gap: The series constantly flirts with this, owing to the busy schedule of franchise lynchpin Tom Cruise. Of late the gap has been gradually narrowing, going from a 6 year pause between II and III, to 5 between III and Ghost Protocol, then 4 until Rogue Nation, and now 3 years into Fallout. The seventh and eight films were scheduled for 2021 and 2022, but the impact of the COVID-19 Pandemic led to delays; indeed, the films were initially intended as a Movie Multipack, but the strain on 7's production due to the pandemic nixed those plans.
Release Date Change: The film was originally set for release on July 23, 2021, but was delayed to November 19, 2021 and then to May 27, 2022 and then to September 30, 2022 due to the COVID-19 Pandemic. Its May 27 release date was given to Top Gun: Maverick. The film will then be available to stream on Paramount+ 45 days after its theatrical debut.
Romance on the Set: A rumored but unconfirmed one between Tom Cruise and Hayley Atwell. Some have claimed that the reports were false since they only appeared very shortly after Cruise's infamous onset tirade, indicating it may have been created to distract from his bad press, not to mention there were reports of him dating Vanessa Kirby during the last installment that were proven false. Time will tell what's the truth.
Troubled Production: The COVID-19 Pandemic has caused major delays in the production of the seventh film several times in a row. It got so bad that Tom Cruise went on a rant against crew members who didn't comply with pandemic time production guidelines, insisting that it was also about ensuring the livelihood of everyone involved. As producer, it was important to Cruise that the production went as smoothly as possible, as a successful shoot could show other studios they could film even under protocols (Cruise even rented an entire cruise liner for the crew to quarantine in relative comfort). That rant was recorded and leaked in mid-December 2020. Even after the rant, though, production still wound up pausing due to additional positive COVID tests in the ensuing months.