Thinking about this more, we're 95% of the way there already - nostr already indexes bittorrent infohashes, and there are already YouTube frontends.
It might help if nostr's bittorrent indexing added a text field for YouTube video ID (watch?v=id)
To credit original creators, the client could also use a new npub for every upload, with an automatically-generated kind 0 profile called "@youtubehandle reposter" (replacing youtubehandle as appropriate)
I might have to make a bounty for this, we're so close. A bounty might not even be needed though, surely I'm not the only one thinking of this?
nostr:note1p0wcgyhk95lcwp2hhwztz3ns7tfmfrd7lrdw7wpyzj4q8xqeks9su95fd7