No need for manual ytdlp! I use TubeArchivist[1] to download channels and then share them with kid's account on Plex. I'm surprised it hasn't been mentioned yet. Great self-hosted solution.
If it’s just the ads that are the issue, paying for YouTube premium would be a similar cost solution, and funnel some money to good creators.
Towards a better Jellyfin solution, I wonder if adding Whisper and an LLM model could transcribe the YT videos and flag any which contains themes that go against parents values.
[1] https://www.tubearchivist.com/