Android TV to Chromecast?

This may seem like a strange request but it is a simple one and I think, a very useful one.

There is a reason that Sony added a feature to be able to play your PS4 from the Vita TV and Vita. Because while it is always optimal to play your games on the best TV you have in the house, said TV is not always available when I can game.

This would be the simplest feature to add to Android TV. All they would really need to do is add the Chromecast app to its compatible list. This would allow it to cast its screen to any Chromecast in the house. And with Bluetooth controllers, mine reach just about any where in my house.

I know playing games while screen casting is not only possible but enjoyable as I have done this using my Nexus 5 and a Moga Pro controller. It rips my battery to shreds but that is not really an issue with any of the Android TVs.

With the addition of one app in Android TVs Play Store, I would instantly be able to play Android games on any TV in my house. Please, Android Dev Team, tell me this is something you will do soon!