I've heard this many times before and don't doubt thats the way doctors feel but it's a little like not monitoring production because you don't want developers chasing down minor production issues.
The lesson a lot of people who are not familiar with public health is that you need to sorta take the long view for these things since we don't make rational decisions.
To bring back your analogy, it's then sorta like requiring an all hands meeting every time your IDE catches a typo. It's still monitoring a something that MAY cause a problem in the future, but to a good enough degree the costs associated with monitering may not be relevant to your actual end goals.