"You eatin' right, boy?"

I suppose that makes sense on a story-level. I'm more certain that they just had you name Tidus because they felt that the players still needed to have the option of inserting themselves into the game. You could not do that with every character due to the voice acting. Also, the player is in much the same situation of Tidus in that we have no idea what's going on at first. Of course, that idea kind of cuts out female players.

Hmm, but going off of your thought, could it be that we (the players) have the ability to choose Tidus' name because we are actually the fayth? We create that identity for him and watch as the dream plays out.