When I had a company managing server farms, I wrote out own ssh client that was brutally scriptable. You could say login here and it would know that in order to get there, it needs to login somewhere else, forward ports, then write su and type the password because of some company policy of the client not allowing direct root logins. We had scripts checking everything and just connecting wherever it was needed without a care in the world.

Then there was version two written by someone else that also logged the content of all sessions to a server so we could show the customer what we did or did not do.

On the plus side, now I login mostly to my machines and I can set it up however I want.