Trump em all
All they really have to do is take the Apple TV and add an HDMI pass through input to it, so that they way you hook it up is _between_ your regular cable TV box and the TV. Normally, it is just a pass through, but when it is time to show something on the Apple TV (for example AirPlay-ing something to it from your iPad) it takes over the TV without you having to switch anything.
In the current scheme, the Apple TV is a second input device. Changing it as above moves it not only to the first tier, but it actually trumps the old first tier device (cable) by being able to cut into it at will.
Selling actual TVs is not a winning strategy. There are too many screen sizes, too many display technologies to maintain. Don't take over the display itself, take over the main input to the display.