A lot of the people on the HTTP WG would have an issue with this statement.Adding to this: HTTP/HTTPS are not stateless, since they are connection-based.
In fact there has been a lot of discussion about the evils of connection-oriented anything in regard to HTTP, especially around authentication (e.g. NTLM).
There are proxies that reuse upstream connections between different clients, the protocol (1.1 at least) is designed to be stateless in terms of each message being independent of others, whether on the same connection or not.
So I wouldn't start a new protocol based on the presumption that HTTP/HTTPS is connection-oriented and not stateless.