When there is low prevalence of a condition, but a non-zero false positive rate of a test, the false positives generated by universal testing can in fact be a net dis-benefit (worry, invasive further procedures, etc) to the patient population as a whole, regardless of cost. This is a well understood statistical phenomenon, and is carefully considered by healthcare systems when advising on testing.
What if in reality the doctors can only say if the probability is above 60% or not? What if some doctors are better than others at estimating probabilities? What if estimates are influenced by financial reasons by some entity like the hospital or insurer?
It's this one
It doesn't matter that some cancers are hard to diagnose. What matters is that some are not hard, especially if you have multiple scans spanning several years
Did you know optometrists now scan your retina during ordinary eyeglasses appointments? They didn't do this in the past because it was too expensive. But optometrists cannot diagnose or treat based on these scans. They refer you to an opthamologist.
Some day your PCP will do the same with MRIs, but only once they are cheap. For now only rich people have this luxury