I think a large part of the problem is a technical and resourcing one, developing a cross-platform game means a lot more work has to go into getting it working, plus QA etc. Then when the game gets patched you have to make sure all platforms get patched the same, and test everything again. It's a bit of a minefield.
Take Quake 3 Arena for example, that's a crossplatform game (PC and Dreamcast), but the PC version kinda left the DC version behind when it came to patches, so you'd have to be running a really old version to be able to play on cross-platform servers.
FPS games don't really seem like a good genre anyway, I'd say driving, beat'em up or sports games could work but maintaining synchronisation could be tricky, probably end up with a situation where you had to really cripple the PC version and make it run at 30fps or some nonsense.
As nice as the idea is my gut feeling is that I'd rather developers focussing on making good PC games than crossplatform ones, the extra effort would be largely wasted.
In terms of console gamers being amazing with a controller, I'm sure some are extremely good with a controller but I still reckon they'd get annihilated by top PC players, they could no doubt beat your average PC player who isn't playing optimal strategies, making dumb moves etc, but ultimately against a player of equal 'nous' they won't be able to compete with the quicker aim from a mouse.