The way I was taught to be on call by a guy I worked with that was also an SRE at a large software company was to "patch the hole in the tire and get it to the service center".

It wasn't about fixing the problem or fully understanding it, but instead making sure the system can run for the time being, get some sleep, and have a more complete triage in the morning. I've found this to work pretty well the past few years.

While I do agree with your sentiment, I'd say that the perspective I've learned about being on call is a big different than the one you've experienced (which may be the more common one, I'm not sure).

So this may end up being a cultural difference between on-call situations.