At the OP.
You make a valid case, but you have some points to consider.
1. LCD TV's are for distance viewing. You would need to sit at a distance to be able to appreciate true HD resolution of an LED or LCD. But at that viewing distance, you really can't type or do anything else except game. Because TV's are not meant to be viewed closer.
If you get a monitor, you could probably game and type and do all other stuff on it quite comfortably.
2. Response times are gonna be a factor, if you play FPS games. The response time if greater than 8-10 ms is going to hamper you when you play FPS games online especially.
On the other hand, the advantage would be definitely that you won't have to get a separate monitor.
I use my monitor actually for gaming and movies, a 27 incher. I think that suits me better.