You mean while your ATV is on you always get a continuity icon?
If so, it would be neat however I can think of some cons. First, swiping up to AirPlay isn't that far from where the icon would be anyway.
Second, I hate to be the "can't trust anyone" type of person but I think that would entice a lot of people on the same network to intentionally or even accidentally mess with the content thats already playing on an AppleTV. If I see a new button on my iPhone the temptation to press it is irresistible.
Third, airplay is content dependent and built into apps. So turning it on is rather useless (unless you want to mirror) until you get into the app you are looking for and the video you want to display queued up anyway.
Thats just my opinion though, I enjoy playing devils advocate.
That would be very useful for me. I like to use my phone to type in search and password fields but I'm generally to lazy unlock my phone and pull up the remote app and log on etc.