Children.
Grand Theft Auto 1 and 2 had an androgyne player character model (well, sprite), and you could pick a representative avatar for it from a selection of men and women of various races and styles. The NPC script was crafted to mostly cater for that, though there was occasionally a slip that may suggest the female characters were lesbian ... or the Big Gay Mobster was actually straight, just a bit camp and perverted.
How quickly we forget.
The question is, whence came the creative or market forces that then distilled the PC into a single gender, race and background?
I'd be interested to see a multifaceted story where you have to play through at least twice, maybe three times as different characters to see all of what goes on, as your backstory and several of the individual missions would be different, and combinations of you would only come together in particular cutscenes or co-op (multiplayer or AI assisted) missions. Which sort of then diminishes the usual argument that allowing different options for player characters in a tightly story-focussed, closed-ended narrative greatly increases the amount of work that has to go in building their models, changing NPC's reactions to them, remodelling bits of the storyline to suit etc without adding anything concrete. Instead, they're all necessary parts of the whole - you can "finish" the game whilst only playing one character, but you don't get full completion or value that way - and thus everyone gets to experience the story from both a familiar and a more alien perspective.
Naturally there wouldn't be any enforced order to the way you do things; you could pick any character to play first (and second, and...). The only difference might be that it may record your actions in particular collaborative scenes and then play them back. The ontological order of things might get a bit tricky (as you may do things in the "first" body that rely on the other PCs being in a particular place or doing certain things, that you then would either be forced to do when in THAT body, lest things get weird), but it could probably be made to work, even if it's a handwave such as "it's a game, whaddya want from us?". Also there's the Assassin's Creed "thing", and that odd one from a couple years ago (Messiah?) where you could take over NPCs' bodies...
I'm sure I've seen RPGs do something similar before, so why not a more action-focussed title?
And anyway, just how many people played Mass Effect as the opposite gender? C'mon.
Edit/PS: Surely there must be a mod for this if nothing else; I've seen people playing GTA as a HORSE after all... and if there's a mod, that implies that it could therefore be replicated in DLC, or an additional "Episode" that comes out later (something GTA is not unfamiliar with)...