If we did not have to deal with the two problems you identify (direct communication peer to peer - effectively the NAT problem with IPv4 - and current firewall practice), then SCTP would be worth a look. I'm not a low-level network expert, and I haven't looked at QUIC in detail, but from the article it seems that SCTP addresses the issues raised in the article. It is a transport protocol on the same level as TCP and UDP, and originally devised for telecoms to transport SS7 signalling information. It's a very good fit to SIP, which is where I came across it.

A long-term connection is established between peers, as for TCP, but this can use multiple redundant paths rather than a single path. Within that connection, multiple independent streams with reliable transmission can exist - which relates to the RPC problem raised in the article, and to situations such as requesting parts of a web page in parallel.

NAT might not be a huge problem, as the protocol does have source and destination ports. One could also envision a proxy on a client device to translate HTTP/TCP to HTTP/SCTP for browsers not yet using SCTP directly. However home routers would probably be an insurmountable obstacle to widespread adoption, and neither Windows nor MacOS currently support SCTP.