There's more than a few channels that upload every episode almost immediately and you can pull the video via a download site by pasting in the URL if you want to archive them.
Some shows like Taskmaster just straight up upload their own shows as well.
I realize now how much WILTY, 8 Out of Cats Does Countdown, and Taskmaster bits I've watched on YT without ever the thought to download and archive them on my Plex server 🤦
It’ll watch any YouTube playlists you specify (I created one called “Save to Plex”) and automatically download them and import them into Plex. Adding videos is as easy as sticking them into your playlist from whatever YouTube client you use.
BBC is funded by the public, thus everything they produce belongs to the public. Kinda. If you live in the UK and pay for a TV licence, you can do pretty much anything with their content.
In any non commercial way. Or even commercial with a licence. They actually ask you to obtain permission to any use, but that's because not all of their content is their own creation and their legal team must work out which parts you can use and which are covered by 3rd parties.