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.
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.
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.