The serious awards already do, although they don't call it Best Duo of course (I think the MTV Movie Awards called first dibs on that
). If two leading performances are deemed worthy of nomination by the members, then they are, and sometimes both win, as happened at the Oscars with One Flew Over The Cuckoo's Nest and Silence Of The Lambs. I can't confirm that all awards do it, but as a general rule it's certainly not the case that a film can only have one nomination for, for e.g. Best Actor, and any other role has to be for Supporting.
By that, I take it you mean motion capture performances, as opposed to, say, Buzz's 'performance' in Toy Story?
This was a big hoo-ha with Andy Serkis and Avatar, but I disagree. A 100% 'live' performance was performed exactly as you see on screen. With a CGI enhanced animation, anything that the actor didn't quite 'nail', such as expression, emotion, voice etc can easily be altered, so you can't be sure how much is digital FX and how much is actual acting.