Airplay doesn't qualify as "convenient" for me. First is the frustration of even getting it to work, and second if I have a phone or mac open, I'll ignore the TV and get sucked into work instead of relaxing.
It's usually two taps, three at most. Hard to see how that isn't convenient. And what's frustrating about getting it to work? It's generally extremely reliable.
AirPlay is the general way to get anything from your phone or Mac to your Apple TV.