The big problem with that is that your eyes are focused on the TV and at the same time you are trying to control it without any tactile feedback.
The beauty of the Xbox controller is that I can feel the position of the stick and buttons with my fingers which makes it easy to make small adjustments. Also things like the trigger buttons allow me to feel how far down I am pressing. Contrast that to a touchscreen where your thumb could easily slide off the area that is emulating the stick without you even realising.
Regards compatibility between iPhones, that's simple enough for games like angry birds but when you get to more demanding "console like" games you get to the point where last years hardware doesn't cut it. For example "Real racing 3" was the game demo'd with the iPhone5, I'm guessing it won't run too well (if at all) on an iPhone 3GS.
The iPhone3GS was released in 2009, the Xbox360 was released in 2005 and still runs new games.
Something between an Android box from Google or a Steam console could come in second. Apple is 95%+ of the way there, they just have to provide a great user experience playing iOS games on the TV. As pointed out, Airplay is unusable due to lag. The output cord gets rid of the lag issue but is too short, cumbersome, and limited.
As for Google or Valve, they have compatibility issues that will make for a rough ride. It could take perhaps a year or two before we started to see an adequate volume of games, and new games, that played natively at an acceptable level.
I agree with the original poster, that this will not be "the next big seismic change." To me this is more about opening the console up to a far bigger market of developers, which helps to hasten to pace of innovation. That will make way for the next seismic change. Or, as I say in relation to my business "A giant leap ahead rather than many tiny micro percentage gains."
I don't know how it is for IOS developers but I have been quite happy how well apps have remained playable and available from iPhone version to iPhone version.