I hear this question all the time - and it sounds like a good idea upfront. Unfortunately, with the way that consoles are, it's just not doable.
Microsoft had a platform under development for a while - several years ago, in fact - that aimed to allow PC and X360 players share servers/games/etc. They scrapped the project early in testing, because they found that mediocre (avg or below avg) PC players would still tend to beat 'professional' console players. The biggest difference was in FPS and RTS, because PC players had greater control with mouse/keyboard than a console player could have with his controller.
I think other developers have looked into that - and, honestly, I think the closest anyone has come, or will come anytime in the near future, is the Minecraft app/console version that let's you play on servers with PC players.
PC mice are much more precise than controller sticks. And the keyboard allows greater control (and more buttons to set/customize) than a controller's triggers and primary keys. Consolers could never play games like League of Legends or Starcraft nearly as efficiently as PC'ers - nor could they play FPS like BF3 on the same level (not to mention consoles can't even HANDLE 64-man servers or maps).
So - while it's a great idea upfront, there would just be a lot of raging on console side because they couldn't keep up with PC. Granted, I wouldn't mind this, as maybe it would bring more people to PC :D But from a business/developer point of view, it could drastically affect console sales in a negative way - and developers are afraid of catering ONLY to PC. They don't want to lose console sales.
