1) From the POV of the patient, how bad / invasive is getting a biopsy? Wouldn't you always want the low-risk biopsy over having discovered a problem too late? From a public health / insurance perspective, I get that you're trying to lower costs and time wasted, which are sadly conflicting goals :-(
2) It's always been so shocking to me that the reaction to "we get false positives" is not "we need to pour money for research into much better diagnostic techniques yesterday" and instead it's "well I guess we'll just not look then".
"How bad / invasive is getting a biopsy?" perhaps you are willing to accept those risks, but you have to also accept the risk that you are getting treated for cancer you don't have. Pathology isn't perfect [0].
Should we invest more in getting better results? Yes, and we are. But, we also have to come up with a risk/benefits strategy for the technology we have now for the patients we have now.
Everything in medicine is risk/benefit because our data and our interpretation of that data isn't perfect.
0: https://jamanetwork.com/journals/jama/fullarticle/2203798
About the same as getting a prostate biopsy, except you can lie on your back instead of on your side while they shove several large hollow needles into your flesh to cut out pieces of a very sensitive gland.
Breast biopsies maybe use sedation and maybe a local bit of lidocaine, maybe not, depending.
It doesn't make a lot of sense to stick a needle in so you don't feel a needle sticking in, but they're different gauge needles.
I think it is both. I think we tell people not to get bad diagnostics while also putting a lot of research into making the diagnostics better so we can tell them to get the diagnostics again.