> Many HTTP proxies only allow traffic through to port 80 and port 443. The benefit of ssh on port 443 is that if the proxy is handed a CONNECT verb,

Thats not how HTTPS works, there is no HTTP proxy for 443. You are in a corporate environment where nothing is let out on port 80, except through their HTTP proxy. However, port 443 is allowed out.

> In fact, this behaviour is what makes HTTPS remain secure when going through an HTTP proxy.

That would be a MITM against https and it doenst work that way.

If you would go over the http proxy to connect to your sshd on port 443, that would be stupid as the proxy would see your connections. Its much easier and better to just connect directly without asking the proxy.