However, there was an update to the protocol, BEP44, that did allow you to update the already-in-progress torrent.
Furthermore, there is a protocol called WebTorrent that swaps out some of the other base protocols for WebRTC, allowing a web browser to participate in the torrents. You could just include a link to the library via CDN. The trouble of course is that bittorrent now relies on DHT more and more (you wouldn't want to have to run a tracker, if you did it'd just be a target of legal attacks)... and WebTorrent can't do DHT (of any variety) well. There was a proposal to allow browsers to be able to do native network sockets, but I think that got turned down by Mozilla (maybe they were more concerned with doing VPN ads or something).
But if you had that, then yes, it might be possible to have something like a "swarmsite" that didn't need to be hosted.