I think the main reason behind this is because of the limited scope of each series's representation, and the goal of showing off what makes each game/series unique. With these settings, adding only the character that isn't the player is usually a bad call because the player is what shows off the game's mechanics. For ensemble casts this gets a bit looser because all of the choices are playable, and show off the mechanics regardless, which is how we got Min Min, and a lot of the reason people are fairly comfortable suggesting Chun-Li over Ryu (in a scenario where Ryu wasn't already in at least).
Rotating casts get kinda odd as the importance of those characters drops pretty quick once you leave the main protagonist. Going with Fire Emblem: Three Houses, Byleth makes the most sense as a choice since he's at the game's center. The three house lords also make sense, as they're major players in the story and tend to be the favorites among players. Students like Lysithea make fairly little sense since while they are popular, they aren't quite as popular as the lords, and there's no garuntee that any given player would even have interacted with them. And any given villain is kind of out of the question since they're either not all that important to the story, a massive spoiler to a new game, humongo, or a combination of these things.
Xenoblade Chronicles is a little better since it's cast isn't like, 1 main character, a handful of support characters, and 30 others in your army, but given how the games focus on a couple of characters over other party members, it would be a bit odd for them to not be the picks. Like, say our reps in SSB4 and Ultimate were Riki and Mórag & Brighid, and then they add Tion in the next game. The characters themselves would be dope, but as picks, not having Shulk, Rex and/or Pyra/Mythra, or Noah or Mio would be super weird. I also think that in a world where we had Xenoblade Chronicles characters, but not the main protagonists, the main protagonists would be some of the most vocally requested characters going into each game.
There's also something to be said about Marth and Shulk being kinda bad at being faces of their series because they aren't in most of the games. This is a little bit less of an issue with Shulk, who does keep making appearances as DLC, but Marth has only come back a couple of times, and is really only the series mascot because of Super Smash Bros. For that reason they can't quite just have Marth, and then add whoever from games he's not in. He definitely does open up appearances from other Shadow Dragon duology characters, but not from things like Radiant Dawn or Awakening.
Honestly that might be the way to go for keeping things fresh with the two series. Whenever there hasn't been a new game to advertize for, throw in a supporting character. Like, instead of Alear, throw in Tiki, Caeda, Anna, Tharja with an altered outfit, or Edelgard to shake things up. I dunno if I'd add anything like Riki, Melia, or Nia instead of Noah or Mio quite yet, since Mio kind of already deviates from Shulk and Pyra/Mythra, and we're only 3ish characters in so the need for a shakeup is questionable anyway, but it is an option down the line.