My lay understanding of the current standard of care is very roughly speaking something like:
Patient exhibits symptom => perform a not-especially-invasive test
Positive test result => invasive test like a biopsy
Positive biopsy result => heavy-duty intervention (although I'm not focusing on this part of the chain in what follows)
Both testing and (certain) symptoms have predictive value, and don't completely overlap. So there's something like this going on:
P(actual problem|no additional information) = really really low, which is why they don't scoop out chunks of every organ to test "just in case" every time you go to the doctor
P(actual problem | [symptom AND positive test result]) = generally high enough in at least some cases to justify the risk of the biopsy, which is why it's the standard of care
P(actual problem | just symptom) = probably not super high, which is why the tests are developed
P(actual problem | just a positive test result) = substantially lower than P(actual problem | [symptom AND positive test result]), so in the general case the balance of risk no longer favors the biopsy
In the broadest of strokes, is there anything I've just said that you substantially disagree with?