Part of the reason is it's hard for them to care when they have to meet so many people in a day. We could easily make it so doctors could take twice as long with each patient, all we have to do is double the amount spent on doctors.
And I don't really think discipline is the best way to make sure things are done properly, a workplace ruled by fear of discipline is usually a dysfunctional one.
It's not really about having faith in "these people", because there is no "these people". There's just people. They have certain skills and training and there's a system they work in, but they're still just people like all other people.
It's seeing that while the system isn't perfect (no system is), it should be about comparing it to the realistic alternative rather than a theoretical ideal.
My kid was misdiagnosed for a virus when he was young, and the medication had the opposite effect to the point where it was kinda dangerous. A trip to the Children's got things straightened out. It's frustrating of course that a mistake was made, and that if we hadn't doubted things the situation might have been tragic.
But it doesn't give me pause about having faith, because no faith is required. I trust the system because the alternative isn't a system where the mistake isn't made, the alternative is my kid having a pretty decent chance of dying of the original problem.
If 10 mistakes causing death are made it would really suck to be one of those 10, but it would suck worse overall if not making an attempt at all results in 1000 deaths.