There are multiple things at play. Clients, and devices (mobile), can change the way that HLS/DASH change the quality, some have reasonably strong specifications. Usually, this is the result of the client being unable to keep up with the quality you're trying to play against the Specification/Configurations.
I'm on desktop website and pretty sure it plays perfectly even in the highest resolution, although I usually go for 1080. The problem is Youtube dumbs down the resolution for every video so I'm not sure what's happening.