As a guy who was also on-call in rotations for many years (which is why I wrote the rant above), the biggest issue with on-call was waking up and not being able to sleep, even when the problem (eg., disk partition filling up) took 5 minutes to fix. The way I dealt with that was coming in late the next day. Like very late. Sometimes at 2pm, to leave at 6. Even if the problem took 5 minutes to fix, my insomnia cost me 4 hours of sleep, so now the company better pay up.

And I encourage everyone to behave this way.