I think some reasons for still using HTTPS as a starting point are the ease of proxying (load balancing), the support for virtual server names, the fact it's easy to use from a web browser, the built-in encryption with TLS.
Plus, for any given large organizational customer HTTP/HTTPS are allowed through their firewall/other network security apparatus, wheras other ports require a bunch of special exceptions from the security people to use. Said people often refuse to give exceptions no matter how reasonable the request might be, so everybody ends up doing everything on port 80 or 443.