When was the last time we actually played with 2 old school, out and out wingers? Unless I'm somehow missing someone obvious, Giggs was our last proper left footed winger, for the rest of the time we've had 1 out and out winger, and another right footed player on the left. And if we play Shinji in the 10 role, who else is going to play on the left. In fact, Rooney would most likely still be here anyway, so he's not getting a clear shot at that role anyway with him around. So that leaves us with Welbeck who plays on the left, who isn't a winger. Young, who will do a step over, cut back onto his right and cross, Shinji who apparently isn't a winger and Januzaj, who isn't a winger. So we're going to turn down Mata because he's not a winger, to play someone who's not a winger instead?
Secondly, arguably our best team of the last decade was a fluid 4-3-3 with Rooney, Ronaldo and Tevez up front. Ronaldo was the only winger there, but even then, he played with a free role and license to roam. We have always had most of our creative threat come from the wings, we have not however always played with wingers in the true sense of the word, to turn down a player of Mata's quality because he doesn't fit this description would be idiotic.
Kagawa has played outstandingly well for Japan from the left, and arguably his best game in a United shirt so far has come from the left, there's no evidence anywhere that he's ineffective playing there. I'd argue that a player like Mata who wants to play like Shinji does would benefit his form, and he'll find it a lot easier to link up with him and drift centrally.
Lastly, we'd get a younger player, in better form, on lesser wages possibly with cash thrown in as well, in return for a player who seemingly doesn't want to be here and hasn't come close to justifying his bumper contract in a long time.