Video quality keeps getting better, which means file sizes keep getting larger, things keep getting more complicated, and software must continue to work harder. According to Googler François Beaufort, the developmental version of Chrome now has a new video renderer that should be able to handle 4K content without stuttering.
You can try things out for yourself by installing Chrome Dev from the Play Store, enabling chrome://flags/#enable-new-video-renderer, and restarting the browser. This should work on your PC and Android devices alike.
Hey look, it now says "Disable." I guess that means it's working.
If your device previously struggled to play 4K60, 4K, or 1080p60 videos on YouTube, try again now. Maybe your luck has changed. This feature is still experimental, so if you encounter any issues, let the Chromium team know.