The downside of scanning for everything is that you'll end up increasing the cost of medicine considerably for extremely little gain. Case in point: breast cancer screenings catch a lot of malignant tumors in an early stage helping many patients before their cases become more serious. But the downside is that it has caused a large number of un-necessary procedures as well raising the costs and - and this is the kicker - blocking the available capacity with cases that would never become serious in turn denying that capacity to people whose cases are serious.

A bit of googling will give you lots of articles on the subject, the same kind of evidence exists for prostate and other cancer screenings as well as other diseases.

For another great book related to your breast cancer example check out The Emperor of All Maladies.

It’s a detailed history of cancer and spends some time talking in detail about how statistics determine at what age preventative testing makes sense given false positive risk.