Wouldn’t separate SSH keys achieve the same?
Separate ssh keys for the user and the admin? Yeah, see point 2, admins should not be remotely accessible.
Really? How, exactly? Break the ssh key authentication? And wouldn’t that apply to all accounts equally?
Keys aren't perfect security. They can easily be mishandled, sometimes getting published to GitHub, copied to USB drives which can easily be lost, etc.
Further, there have been attacks against SSH that let malicious actors connect remotely to any session, or take over existing sessions. By not allowing remote access on privileged accounts, you minimize risk.
Forcing a non privileged remote session to authenticate with a password establishes a second factor of security that is different from the first. This means a cracked password or a lost key is still not enough for a malicious actor to accomplish administrative privileges.
A key is something you have
A password is something you know
So, by not allowing remote privileged sessions, we're forcing a malicious actor to take one more non-trivial step before arriving at their goals. A step that will likely be fairly obvious in logs on a monitored machine.
I strongly disagree with your premise. Separating authentication and privilege escalation adds layers of security that are non-trivial and greatly enhance resilience. Many attacks are detected and stopped at privilege escalation, because it happens locally before a user can stop or delete the flow of logs.
No you cannot. A non privileged user doesn't have the access necessary to run a program that can accomplish this.
Once again, you didn't privilege escalate, because once you have a foothold (authentication) you don't have the necessary privileges, so you must perform reconnaissance to identify an exploitable vector to privilage escalate with. This can be any number of things, but it's always noisy and slow, usually easy to detect in logs. There is a reason the most sophisticated attacks against well protected targets are "low and slow".
You're ignoring my points given regarding the risks of compromised keys. If there are no admin keys, there are no remote admin sessions.
Spoken like someone who has never red teamed or purple teamed. Even admin accounts are untrusted, given only privileges specific to their role, and closely monitored. That doesn't mean they should have valid security measures thrown away.