With HDMI on a phone, not only you have to go to your TV to plug your phone to it, but you then can't use your phone anymore or switch tasks easily. Also HDMI cables and connectors are usually pretty stiff which doesn't really work well with a light device. What I mean by that is that your device is kind of flying around on your TV stand until the cable finds a good position. (this doesn't happen with heavier things like a BluRay player)
AirPlay, in principle, (I haven't tried it yet) would bring the same benefits wirelessly.