Send to AppleTV, and redirect playing stream

When I click the watch button on a show on my iPhone, Channels gives an option to send to my Fire Stick. Would be nice to have this "send to" feature for ATV as well.

It would also be very nice if you could take an active playing stream on your phone and "re-direct" it to another device, without stopping and re-watching it. The YouTube app works this way.

The ATV will show up as an option if the Channels app is active on the TV.