Earlier quoted context omitted.
This is infuriating as a parent. My daughter likes certain videos, and I have to write down the titles of her favorite videos to search for them every time she asks for them. (We watch YouTube on an nvidia shield). I honestly don't understand how this restriction makes sense, it all seems punitive.
At least on the web version, funnily enough you can do add them to a playlist. If you do it from the search results list, not the video permalink. You could also try if an alternative YouTube client like NewPipe works on the Shield, and brings more useful bookmarking features? (Another option would be downloading them, again with NewPipe or on a PC, and keeping the files somewhere)
Your advice is eminently practical. I already have a PLEX server, I could just youtube-dl the videos/channels she likes.