> You always need someone standing by in case of some terrible disaster that cannot be handled automatically.
If it's a really terrible disaster, a once-a-decade kind of thing where everything goes haywire and you need as many staff as possible to get online ASAP, then yes. But aren't we talking more about the kinds of "disasters" that happen once a month or so, and can be handled by a few staff (not waking up the whole team). To me that sounds more like just staffing for normal operations.
At large engineering companies this is typically handled via literally having someone standing by, i.e. formally on duty, rather than having off-duty employees be on pager duty. There'll be at least a bare-bones staff on the after-hours shift (probably not in all offices, but in some kind of 24/7 operations center), enough of a staff that reasonably foreseeable things can be handled. Of course there are some pros and cons to that from an employee perspective. On the one hand the night shift isn't that pleasant, but on the other hand your responsibilities are at least formally limited to 40 hours/wk; if you're on night shift one week, you don't come in during the day, or carry a pager during the day.