which is not very helpful if you for example want to run git via ssh or similar commands on the target server.

There's places where there are two alternatives: agent forwarding or copy the key. Using ssh agent forwarding allows me to use a smart card for the key. It still has it's problems but it's much better than having the key on the remote machine - for example the use of a smartcard mitigates this vulnerability since the key never enters the process memory.