Even in family practice, it’s not uncommon to be able to get a call back from the on call doctor at the practice on weekends or off hours — if you’ve got a situation that maybe doesn’t warrant the ER, but you’re not sure if it can wait until Monday.
Only if you're dying.
Come in late Friday and you're going to be sitting in a bed until Monday even if your gall bladder is about to explode.
The point was that "on call" is specifically confined as an expectation only to certain types of doctors or under very urgent circumstances.
In addition, doctors have extra special dysfunctions like "too many hours in a shift".
However, many of these are because doctors also have been fighting various efforts to teach more of them which would enable distributing the required extra labor across more people.
In addition, I had something similar happen where I wound up needing Interventional Radiology to insert a drain--again wound up waiting from Friday to Monday morning.
I'm sure some of those doctors were "on call". However, nobody was calling them in unless I started dying.
But what you’re talking about is a person whose job it is to be oncall. It’s the equivalent of an SRE, rather than a SWE. They’re not doing it because they believe in “you build it, you run it” or anything like that.
No they don't.
I know plenty of people who have had to sit around for 8+ hours because the particular type of doctor is not available. The on call only really applies if you're bleeding out.
In my 20+ years of development and support, there has only been once that I was paged due to an actual catastrophic failure. Most are because shitty "SREs" wants monitoring on everything, even if its stuff that I have no control over.