Can Apple do that stuff? Of course. Does it make sense? Hmmm...
Making mobile-oriented iDevices THE video source solves a number of problems in terms of securing deals with the various Studios, etc (just leave that to the existing deals already made with those Studios by cable/satt providers, etc). Of course, this won't help some of dreaming of cutting the cable/satt subscription to get the Apple replacement subscription (but that's beat to death in other threads).
It still doesn't solve the mobile problem. iDevices leave home with their owners. If someone is single living alone- no problem. But if someone has a family or roommates sharing that television, the crucial video feeder will sometimes be there and sometimes be out with the owner. That's not going to work well (unhappy family back home).
This would mean having to dedicate a mobile iDevice to being immobile (always at home). Sounds easy enough. But then the real cost of a "whole" TV is the cost of the TV box (or this thin bar) PLUS the cost of an iDevice to dedicate to it.
And then you have the problem of other members of the family wanting to make that immobile iDevice mobile again. The analogy I'll use is the old, tired one of wanting a cell phone just for emergencies, getting one for emergencies and then it getting used for non-emergencies. Members of the family or roommates are going to want to use the dedicated iDevice for stuff other than feeding the TV video. And that means others at home will (again) be locked out of using it.
So again, the "solution" becomes having to buy everyone in the home an iDevice so there is always a "good remote" available no matter who is in or out. This works for a family (though it makes the whole TV proposition that much more expensive) but it gets messier for the roommate situation.
Bottom line: whatever this next-next Apple TV thing is going to be, I'll be surprised if it has ANY dependency on an iDevice. Sure, create fantastic apps for iDevices to add all kinds of functionality, but don't make it depend on an iDevice also being in the home. Else that comes with all kinds of messy social and economics issues... except for the single people living alone.