You basically end up with a half-assed, buggy, and potentially insecure reimplementation of HTTP running over web sockets running over HTTP at that point.
Are you going to do session management and identification by issuing a unique identifier as well? Is that unique identifier going to be valid in perpetuity or have a an expiry date? Is it going to be valid and secure across all sub-domains or will it be prone to cross site scripting attacks?