Overscreening is recognized as a problem among epidemiologists.

Rationality does not specify values. I rather suspect that the cost-benefit analysis that epidemiologists look at is quite different from the cost-benefit analysis that individuals look at.

these screenings are either a problem in themselves, or that the information from the screenings can lead people to irrational behavior

LOL. Don't bother you pretty little head with too much information. No, you don't need to know that. No, you can't decide what you need to know and what you don't need to know. X-/