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.
If I get into your non-privileged account I can set up a program that acts like sudo
No you cannot. A non privileged user doesn't have the access necessary to run a program that can accomplish this.
And even if they do it’s too late anyway because I’ve just compromised root and locked everybody out and I’m in there shitting on the filesystems or whatever. Because root can do anything.
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".
And if I can’t break into your non-privileged account then I can’t break into a privileged account either.
You're ignoring my points given regarding the risks of compromised keys. If there are no admin keys, there are no remote admin sessions.
These artificial distinctions between “non-privileged” and “superuser” accounts need to stop. This is not good security, this is not zero trust. Either you don’t trust anybody and enforce explicit privilege escalation for specific things, or just accept that you’re using a “super” paradigm and once you’ve got access to that user all bets are off.
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.