On the protocol level, there is a huge knowledge and API momentum that makes any protocol that fundamentally differs from HTTP an uphill battle for adoption. Whatever changes are made to HTTP, if it is too different from the application POV, it will linger behind.
Same thing about tunneling. It may not be elegant, but it's the way to fight the system. You won't change IT behaviour with a protocol change. One possible way to work would be to make new version oF HTTP have a working mode that reduces overhead to a minimum for any tunneling operation.
(The same argument hold to SCTP vs TCP.)