I can see how SSH could be used for authentication on the web. And I have no doubt that it would be sound out-of-the-box. But I am not sure what you mean by your last sentence. Do you mean that authentication targets are gated and only reachable by establishing a tunnel via some kind of forwarding?
Aside from the wonderful possibilities that are offered by using port forwarding of some kind, you could also simply use OpenSSH's ForceCommand to let users authenticate via SSH and then return a short-lived token that can then be used to log into an application (or even a SSO service).
I guess no one uses SSH for authentication in this way because it is non-standard and kind of shuts out non-technical people.