There are numerous non-HTTP protocols used successfully on the Internet, as long as they run over TCP or UDP. Policing content running on TCP port 443 to enforce that it is HTTP/1.1 over TLS is actually extremely rare, outside some very demanding corporate networks. If you wanted to send your own new "HTTP/7" traffic today, with some new encapsulation over TLS on port 443, and you controlled the servers and the clients for this, I think you would actually meet minimal issues.

The problems with SCTP, or any new transport-layer protocol (or any even lower layer protocol), run much deeper than deploying a new protocol on any higher layer.