I'm not sure I get your idea of 'not suited to fighting games' when it comes to Smash Bros. in particular, since Smash Bros. is most certainly not your traditional fighting game.
When has being suited to fighting games ever stopped Sakurai with some of these outlandish picks? You really think characters like Pac-Man, Ice Climbers, Isabelle, Duck Hunt Dog, Wii Fit Trainer, Piranha Plant, R.O.B. and Mr. Game & Watch are suited to fighting games?
You're talking about a game where you can put a chubby green dinosaur up against a space bounty hunter. Or team monsters and demons up against talking animals with space laser guns and a metal man. Or a vampire hunter against a plant. Or an electric baby mouse alongside a fallen angel with one wing. In a roster as huge, diverse, and outstretched as Smash Ultimate, either every character is out of place or none of them are. That idea is absurd. If you told a group of college kids back in the late 90s-early 00s this would happen, they'd ask you what you were smoking and where could they get it. The whole concept of Smash Bros. is ridiculous and outlandish. That's what makes it Smash Bros.
What I mean is does the character lend themselves to a moveset that would be fun to use.
Like with Pikachu, you can understand how it would be intrinsically satisfying to go around zapping people. Ice Climbers have hammers that can smack people around. With Phoenix wright, it's hard to see immediately how he'd be fun to use. He's a lawyer... he walks around and does normal lawyer stuff. Even in UMvC3, which is I think the best you can do with him, I don't find him especially fun to play as, beyond the novelty of putting Dr. Doom on trial.
Basically, I just don't think Phoenix would be fun to play as. With a character like Mega Man you can imagine all of the abilities and powers he could use, so it's easy to see why people wanted him in the game. With Phoenix Wright, I just don't anticipate him being really fun to use in Smash. I could be proven wrong, but I'm not seeing it.