We see in the US the astronomical cost of health care compared to, well, everywhere else on earth. And that is partly because of inefficiencies like screening when it isn't called for.
Screening is recommended because population level statistics indicate it should be done. Hence pap smears, mammograms, colonoscopies at certain ages. Hence also screening for a broken nose and for bleeding in the brain and fractured skull when a patient presents after falling flat on her face on a tiled floor. Also heart monitoring. Yes, dehydration might have caused my fainting episode. But so also could a few other conditions, and some of them are serious.
It's the pricing model that is the problem. Screening itself is an excellent idea because it often identifies issues before they are medical problems requiring intensive and expensive treatment that is possibly going to be too late to be effective. Curing people before they become gravely ill is preferable to throwing the kitchen sink at an illness and still failing to prevent death. In stark terms, curing a patient is the only way not to waste money.
There are also issues with false positives - screening doesn't always produce the correct result. If you get screened a lot when the chances of something being found are small, the number of false positives will be higher than if people are only screened when clinically indicated, but the number of true positives that would not have been found by only screening where clinically indicated will be small. With some conditions, the impact of following up a positive screening result (a biopsy, say) can have some negative impacts. The negative impact of follow up on people who have false positive screening results over a large population can sometimes be worse than the impact of the few true positives that are missed.
You are talking about a tiny proportion of results, many of which can simply be retested, without a biopsy if there is any question about reliability. 'Some negative impacts' of a biopsy are not serious enough or widespread enough to warrant dropping, for instance, colonoscopies or pap smears or mammograms, from the list of highly recommended tests at certain points of one's life.
It seems to me that you are saying that for the sake of avoiding a tiny, tiny number of false positives and a tiny fraction of negative experiences in confirmation investigations, screening in general should be ditched.
You are allowing pricing issues to set aside the interests of science.