I agree with your criticisms of BitTorrent vs older P2P sharing. The closest successor I know of might be Tribler. I haven’t used it so I don’t know how the uploads are - and it still has many drawbacks/inefficiencies relating to hashing/duplication because it’s torrent-based. But it does contain search, and the ability to share without a website indexing it. It’s kind of like eMule: torrent/tor edition?