They made such a big deal about being able to enjoy multiplayer using an iOS device (presumably though the Remote App). Had my husband come over so that we could play Crossy Road together like at the keynote... but no 2-player option or ability to use phones. It really seems like Apple shipped this before it was really ready. Steve would have never allowed that.
Crossy road is played multiplayer through a iOS device with crossy road installed not through the remote app. Launch crossy road on both the Apple TV and iPhone then on the right side of the screen press the control pad icon and it searches for the Apple TV then you can play 2 player.
There were many quality issues that happened over the years when Steve ran the show. Were you not around for the launch of MobileMe? Good lord, Walt Mossberg even panned it. Or the first gen iPod nanos that scratched if you just looked at them wrong? Antenna-gate? First gen Intel Mac issues?
Steve allowed a lot of not-quite-ready things to ship.
Bringing him up doesn't do any service to the points you were trying to make, IMO.
It's not really compatible with the ATV 4 in any meaningful way. But if you select your library and start playing a song. Then tap the AirPlay icon and choose the Apple TV, it will stream music from your Mac to your Apple TV.
That at least gives you full control over the playback (track selection, play/pause skip and so on) and doesn't tie up your iPhone. (Because it's streaming from your Mac it will continue even if you switch your iPhone off or start doing something else on the iPhone.)