The controller is fine for FPS games and HDTVs have the same amount of lag that PC monitors do.
Um... no. No, and also, no. If you think a controller is fine for FPS gaming, you are not very good at FPS games. This is a fact, not an opinion. The controller does not offer the precision that a KB/Mouse offers, plain and simple. The best console player in the world of any given FPS game will get schooled by an average PC KB/Mouse player. The speed and precision just aren't there with a controller.
Anyone who has progressed beyond just sitting down to a quick game of deathmatch to something resembling competitive play will tell you straight out that a controller is a joke for serious play. The fact that you think an controller is fine for FPS indicates you've not progressed beyond the occasional game with your friends on a Saturday night, therefore, you aren't really qualified to make a judgement call as to whether or not a controller is "fine for FPS."
Many HDTVs introduce a lot more lag than a monitor, so your argument there is also false. Although, many PC monitors do have quite a bit of lag. Again, if you're buying a monitor for gaming, you should make sure you get one with low latency.