The details of the complexities change, but the complexities are still there. You still need adoption by multiple parties, you still need to solve the application level challenges that HTTP solves (including, most importantly, secure communication over an open network), and you still need tooling to understand the protocol in flight, including its failure modes, to debug an application built atop the protocol. And you lose the utility of libraries and infrastructure built around using the other protocol.

The opportunity cost to do that with a brand new protocol instead of taking advantage of HTTP's flexibility to build new protocol atop HTTP is high.