Apple TV lets you watch all three (iTunes, Netflix, and Amazon Prime).
Airplay is a thing.
Airplay is a thing.
How is that a "workaround"?
An iPad, iPad Mini, iPod, or iPhone is your remote - the AppleTV remote is horrible anyways and I've personally long ago tossed it. Fire up your new remote and play anything you like... it's incredibly simple.
I'm sure your solution works fine for you. But be careful in projecting your use case to everyone's. :)