Surely the correct response for noninvasive tests is to run the test, and raise the threshold for intervention?
https://my.clevelandclinic.org/health/diagnostics/12360-hydr...
Software developers often have this unrealistic fantasy about how things ought to work in medicine and biology. They reality is far messier.
Also yes, you're right about having good estimates for medical tests.
Mainly I take issue with your claim that "Running most tests twice won't necessarily give you any useful additional information." As long as it is directionally associated with the thing you're trying to test for (i.e. it has any medical value at all), then running it twice absolutely should give you additional information. "Not necessarily" I guess is true, but again, probability gives us the tools to reason about situations like this even if we can't estimate population parameters reliably.