I don't know if Fuuka protecting herself with her Persona is more of an embellishment than completely redesigning Himiko, considering that shielding people is a thing that Fuuka's Persona is established to actually do.
By defensive I meant like a parry type character, like Exdeath in Dissidia or something.
And it's fine if you don't actually like Fuuka enough to be playable, she's almost certainly one of the least popular party members of P3 + 4, but beyond that I don't see any reason why she shouldn't beyond personal distaste or apathy, and those reasons certainly didn't stop Ken Amada from being playable with a complete redesign. It's not a question of impossibility, it's a question of desirability. Second thing is perfectly reasonable (though I still think it's wrong to leave her out) but the first I reject completely.
And I don't even like Fuuka, what am I doing.
With all due respect, I think it's a little disingenuous to predicate your argument on desirability. There are several practical things to consider when adding a character to arena. Moveset potential and feasibility are HUGE factors to consider. According to Wada, creating fighters with a unique sense of style was P4A's mission statement. Bringing the skills they used in Persona 3/4 to life and making that an integral part of their moveset was also an important. With that in mind, it's clear that Fuuka simply does not lend herself to being a playable fighter in Arena. Her moveset potential is practically nonexistent; I mean it's pretty telling when nobody can't think of serious moves for her normal attacks. It's a result of her character being too damn barren (especially when compared to the rest of the Persona cast.) On the Persona front, there's nothing she does that Rise doesn't.
With Rise, they could fall back on the fact that she's an idol (and the fact that her Persona can simply do more things than Fuuka's). Fuuka has next to nothing on the physical front, and is limited on the Persona front. Even if she got a completely redesigned Persona, it would be difficult to come up with a moveset for Fuuka
herself (can you think of regular skills for Fuuka to use?). I'm not even hating on her character; her character just isn't conducive to a fighting game.
Incidentally, popularity didn't affect Ken's inclusion in Arena, because had an
entire moveset to draw from (and Koromaru, to sweeten to deal). Fuuka simply can't be compared to him. I'm fairly certain that Fuuka was decently popular in Japan (if the Persona popularity poll is anything to go by)
EDIT: Wait, since when could Fuuka's Persona shield people? It learned a set number of scanning related skills, and outside oracle, it had the same skillset as Rise's Persona.