Jellyfin + ytdlp + playlists = pretty good, in general. and avoids ads; the ads are worse than almost anything else you can find.
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.
I built this with Jellyfin and Home Assistant for my kids: https://github.com/philips/homeassistant-nfc-chromecast