Ryota Niitsuma, producer for Tatsunoko vs. Capcom, says the company did have plans to put the famed juris doctor in the lineup, but ran into problems because his OBJECTION! was just too powerful in English.
Niitsuma told NGamer magazine that Capcom wanted Phoenix Wright, and Franziska von Karma (for her whip), in the game, but ran into trouble with Wright's move set.
Because Phoenix Wright only has one move, 'Objection!', we struggled. We designed a move for him: when he says objection, the actual writing attacks the opponent. However, 'objection' in Japanese is 'igiari' - it's four characters, whereas 'objection' becomes ten [sic. It's nine, actually.] When we localize, the balance of the game gets destroyed because the move becomes bigger. There'd be no way of avoiding it! We had to remove him for these reason. In the future, it is one of our aims to get him in.