I switched to using Moonlight to stream rather than Steam's built-in RemotelyPlay months ago. It was just absolutely unusable; not a bandwidth issue, had that in spades. The problem was that it would either not connect, connect to a blank/green screen or the audio/video would randomly cut out. It would work maybe a fifth of the time, and if I had to reconnect for whatever reason, it would absolutely always fail.
Moonlight? It worked out of the gate, and has never failed despite running on some beefy encoding settings since I have very good WiFi with next to no interference from neighbors.
I desperately want Steam's own offering to be better though. Not having to install a second tool, and to just connect from Steam directly would be a much more polished experience.