When you want to connect from A to C through B, SSH agents and key forwarding don’t save you the need to type in the command to ssh from B to C – it just saves you the need to manipulate more keys if both C and B can be logged into using your key chain on A.

What I’m trying to solve is how to seamlessly ssh from A to C without starting a shell on B and typing commands there. The proxying is transparent enough that if you later login to B, you won’t see your proxy command in the shell history (which may or may not be useful to you).

Also, if this is something that people do a lot in your organization, it will be better to set something up on the firewall itself instead on relying on each person configuring proxy commands on their system.