The main issue you run into is that the web is designed around client-server communication; you can do peer-to-peer communication in theory but because of NAT and firewalls, many of those end up not being peer to peer in the end.

Plus, if you want the data to persist so that two people can collaborate even if they are never online at the same time, you need a server anyway.

CRDTs as data structures support peer-to-peer, it’s just that in many use cases that aspect of CRDTs is not needed.