Most don't create new keys per server machine but that's not the issue. I don't bother, I create a key per client machine on my side.

Server gets compromised once, admin logs in and fixes it, admin logs in next time and the backdoor compromises it again.

That's all this is. If you can get in once, it's a spot you can leave a backdoor that many admins will miss. That's it.

Admins don't generally copy that whole file around, they usually copy and paste the lines they want. Also I generally copy and paste it from my workstation, not another server.