To a certain extent, the typings of some (not all) of the Warlords are quite illustrative of their historical fates/interactions with each other (or if it wasn't the intention, they do provide thoughtful notes):
The Hero's/Heroine's and Oichi's Normal typing serve to harken Oichi's pairing with Azai Nagamasa (as has been recounted countless of times in the main page).
The typings of Nobunaga, Mitsuhide and Hideyoshi: Dragon, Ice and Fire, which are weak against each other in succession. Mitsuhide defeated Nobunaga, and Hideyoshi eradicated Mitsuhide.
Hideyoshi's acquisition of Reshiram fits into this as well: while he is technically weaker than Nobunaga, he was nonetheless able to accomplish what he wasn't able to, and he also managed to become as prominent as Nobunaga himself. The relationship between Zekrom and Reshiram, previously emphasized in Pokémon Black and White only highlights this.
With Nobunaga rocking Zekrom and Hideyoshi packing Reshiram, one wonders why Mitsuhide gets Articuno instead of Kyurem. Spoiler-dodging for the Version 2 games aside, Hideyoshi remained loyal to Nobunaga, while Mitsuhide turned on him - hence, the differing legends.
Tokugawa Ieyasu's Steel-type specialty highlights his relationship with many Warlords too: Hideyoshi's Fire-types definitely keep him in check, and Ieyasu was indeed only able to assert supremacy in Real Life after Hideyoshi passed on. His weakness to the Warlords of Terrera are also illustrative: Ieyasu badly lost to Takeda Shingen (Rhyperior and Groudon) at the Battle of Mikatagahara, and he was (allegedly) almost killed by Sanada Yukimura (Charizard) in some of the battles of the Siege of Osaka. Finally, his Steel-types are pretty much weak against Yoshihiro's Fighting types - which somewhat foresees the fact that the conflicts of the Bakumatsu, initiated by Shimazu Yoshihiro's descendants (the Satsuma clan), were instrumental in the downfall of the Tokugawa shogunate three centuries later.
Yoshimoto's Bug-types (especially Forretress) are pretty much laughable if you will pit them against Ujiyasu's Rock types and Nobunaga's Dragons. He was never really able to defeat Ujiyasu in battle in Real Life, and he was ignominiously eradicated by Nobunaga in Okehazama. The generic warrior Ujizane, branded this game's Joke Character (who can only carry one Pokemon and his perfect link being Pineco/Forretress), is Yoshimoto's historical son, and has even less respect going for him among historical records.
Muneshige's Flying types, being effective against Yoshihiro's Fighting types, somewhat recall that the Tachibana were regular and aggresive rivals of the Shimazu. That Violight, Ginchiyo's kingdom, is more composed of Electric types also suggests how the Tachibana clan never really managed to take an edge against the Shimazu.
Kenshin and Shingen, despite being portrayed as legendary rivals, deal neutral damage to each other - a reference to the fact that their conflict was never really settled after five battles in Kawanakajima (which also points out as to why their stories involves them in a race to score five victories against each other). Related to this, among the generic Warriors is a man named Haruyuki - who corresponds to Shingen's celebrated strategist Yamamoto Kansuke. Haruyuki's Perfect Link is Rufflet & Braviary, which deals super-effective damage to Kenshin's Gallade - pointing to how Kansuke/Haruyuki's strategizing and advice to Shingen was also instrumental to the Takeda's keeping up with the Uesugi (a viewpoint advanced in fiction by Yasushi Inoue's novel Furin Kazan, later to be adapted into an NHK taiga drama).
Masamune's Flying types are definitively weaker compared to Ieyasu's Steel types - referring to how Date Masamune, despite wishing to unite Japan on his own, never really managed to one-up the Tokugawa.
Ina (real-life name Komatsuhime)'s link is largely Water-types, especially Empoleon - which gives her an edge over Yukimura's Charizard. This somewhat fits into the fact that, in a domestic dispute between Komatsuhime and Yukimura (the former having married Yukimura's brother Nobuyuki, and is thus technically his sister-in-law), she was apparently able to intimidate Yukimura (and the rest of the Sanada) into backing out.
Ujiyasu's Rock types (apart from his effectiveness against Yoshimoto), while powerful, are not exactly strong against Shingen's Ground types. Similarly, Hojo Ujiyasu was never really able to take an edge against the Takeda while Shingen was still alive. They are also weak to Valora's Steel-types, foreshadowing the fact that Toyotomi Hideyoshi's side (Ieyasu being one of his major generals) would eventually defeat the Hojo in the Siege of Odawara.
The battle between the three kids (Mitsunari, Kiyomasa and Masanori), as highlighted in Genius Bonus in the YMMV section, was indeed illustrative of the fact that Mitsunari is (allegedly) contemptuous of both Masanori and Kiyomasa in Real Life - illustrating how Mitsunari's Scizor easily beats the other two's basic Pokemon. However, their Perfect Links tell another story - Mitsunari's Bisharp and Masanori's Krookodile are, qualitatively, no match to Kiyomasa's Haxorus, harkening to the fact that Kiyomasa's station is better than the other two during Ieyasu's rise to power (Mitsunari dead for siding with Hideyoshi's son Hideyori, while Masanori's holdings and influence were reduced during the Tokugawas' reign).
Among the generic Warriors, a man named Yoshiteru gets Beldum/Metang/Metagross. While not necessarily unique, it is remarkable for a generic character to get a pseudo-legendary. This makes sense, in a way, since he is the stand in for the supposedly last-competent Ashikaga Shogun, Ashikaga Yoshiteru, whose tenure as Shogun foresaw the rise of conflicts of the Sengoku period (for whom this game was based). Being the reigning Shogun during the time, one would have expected him to have a major role. However, his efforts in Real Life were overrun by the fact that his authority is ebbing away - no less by another ruthless daimyo, Matsunaga Hisahide, who sided with Nobunaga (also existing in this game as a generic Warrior and even shares Nobunaga's Perfect Link of Deino/Zweilous/Hydreigon, which checks Yoshiteru's Metagross).
Kanbei's perfect link Pokemon being Lampent and Chandelure is Fridge Heartwarming if one is familiar with Samurai Warriors 3. In that game, as Hanbei succumbs to his illness, he declares that he will always be a light watching over Kanbei. Kanbei's perfect link pokemon is a candle ghost.
Why is there a Simisage, a grass type Pokémon, battling among Nobunaga's dragons in the main story? Because Nobunaga's Pokémon, Zekrom, can't effect ground types and Simisage is there to counter them.
The reason Hideyoshi is paired with Infernape is almost obvious if you remember that Nobunaga's nickname for Hideyoshi was "Saru", ie. "little monkey".
The fact that Mitsunari, Kiyomasa and Masanori goes out of their way to give your character (the Hero) a tutorial when you begin the game, even if a bit dismissively gains a bit of interesting historical subtext if you follow the "Hero = stand-in for Azai Nagamasa theory". Mitsunari's family, the Ishida, were formerly retainers of the Azai, who were forced to lay low before they eventually went under the service of Hideyoshi.
The inability of both Ginchiyo and Muneshige to promote unless they are in separate, non-adjacent castles, their contrasting types, and the seemingly-less romantic endings of their routes (where they almost always are apart) points to a sad historical fact: that they eventually divorced. Ginchiyo, however, made her mark in history by helping out her ex-husband Muneshige to survive the tail-end of the Battle of Sekigahara - a remarkable thing for a divorced wife to do, and is alluded to by the fact that she values Muneshige (even if they disagree) for the duration of the game.
Okuni was the creator of Kabuki theatre. Thus, it makes sense that her perfect link is Volcarona, as it uses Fiery Dance!
The legend. Sounds like a basic Gotta Catch 'Em All plot, but remember these are actual nations we're talking about - which are presumably populated by hundreds of people. How would you like it if your country was invaded on a daily basis just because everyone wants a shot at the Legendary Pokémon? To be fair, Oichi notes this in-universe.
It goes a little beyond one in-universe mention. Stopping this whole system is Nobunaga's true ambition.
The time-system being based on months means that the game takes years to complete in-universe. The hero could easily spend 20 years trying to defeat Nobunaga. 20 years at war for an entire continent.
Then again, the battles in this war tend to be, at most, six-on-six Pokémon battles. On top of that, they're often in secluded areas. They're really not that much more terrible than battles in the main series.
The real Fridge Horror is the aftermath; all you have to do to become the reigning Warlord of a kingdom is to defeat the previous one in a glorified Pokémon battle, no leadership skills, experience, or prior knowledge required. The citizens of each kingdom are probably praying to Arceus each time their Warlord is challenged, either wishing their Warlord isn't replaced by someone incompetent, or is replaced by someone who is, depending on the situation. Which, when you think about it, is also doubling as Fridge Brilliance—as many commoners and civilians during the Sengoku period almost always stood by daimyo who could provide stable leadership.
Hanbei's ending is this and Tear Jerker. In the game, Hanbei is portrayed as a young boy. In real life, Hanbei died of tuberculosis during an important battle that Hideyoshi instigated to another nation. In the game, after he wins the junior battle, he starts coughing uncontrollably. Hideyoshi asks if he's sick and Hanbei just replied he got too excited. Kanbei looks at him and Hanbei glares at him telling him "Don't say anything" before switching the subject. It's very obvious that the ending implies that Hanbei probably died shortly after the whole battle and what's made worse is that unlike his real life counterpart who died in his mid thirties, Hanbei is at least a teenager and would probably die even younger than his real life counterpart.
Regarding that last part, Hanbei states that he's older than Kanbei in the latter's story. So while he would have had a longer life that still doesn't eliminate the depressing part of the tale.