But is it completely impossible to separate the monitoring and equipment/management?

Stupid example like the equipment itself is not networked, but you could watch via a webcam and/or get metrics via image recognition.

Maybe it's safer just to have somebody work the night shift.

No, and it's not strictly impossible to correctly build out a SOC / SIEM and ingest all the logs you want and pay for the right engineers to make sure it all works correctly. But damned if anyone manages to do a great job in this area. It's too complex and too expensive, so almost everyone settles for "best effort."

A lot of problems are easy conceptually, but we can't manage to tackle them.