Meanwhile in the enterprise, 80/443 is frequently locked into a particular (cheap) HTTP proxy server that can't manage basic features of HTTP correctly.
Furthermore, I'm assuming you don't expect applications to work only in the confines of a lan.
There are strong reasons why HTTP is highly favoured for communication protocols. Heck, whole industry protocols have been scrapped in favour of HTTP-based ones for this problem alone. See RTP and why it has been abandoned by HTTP-based protocols such as MPEG-DASH, and why the industry made it their point to develop a whole new video streaming protocol based on HTTP.
That is patently false. The problems isn't caused by not controlling the client. The primary problem is that they don't control the network, which means each and every single node between client and server, and HTTP reduces or eliminates the chance that one of those nodes doesn't cooperate.
Actually, it is.
Furthermore, I'm assuming you don't expect applications to work only in the confines of a lan.
There are strong reasons why HTTP is highly favoured for communication protocols. Heck, whole industry protocols have been scrapped in favour of HTTP-based ones for this problem alone. See RTP and why it has been abandoned by HTTP-based protocols such as MPEG-DASH, and why the industry made it their point to develop a whole new video streaming protocol based on HTTP.