[PeterisP]

I've seen the exact opposite configuration where it's not possible to avoid SSHing from one remote server to another due to network segmentation, as on the network level it's impossible to access any production system directly via SSH but only through a jumphost, which obviously does not have a browser installed.

[hamburglar]

You don't need the jumphost to do the auth for the target host. You use -J and the auth happens locally and is proxied through.