This is true for e.g. any visit to the doctor. Are you saying that it's irrational to go for medical checkups?
In the cancer screening case, what do you think does the cost-benefit analysis say?
It would be irrational to go for medical check ups when they aren't necessary - if you did it every 3 days, for example.
I'm looking at this from a birds eye view. A lot of people get unnecessary screenings, which tell them information which is not worth acting upon no matter whether it says that it is positive or negative, and then start worrying and getting unnecessary testing and treatment. Information is only useful to the extent that you can act upon it.
Jason Mitchell is [edit: has been] the John L. Loeb Associate Professor of the Social Sciences at Harvard. He has won the National Academy of Science's Troland Award as well as the Association for Psychological Science's Janet Taylor Spence Award for Transformative Early Career Contribution.
Here, he argues against the principle of replicability of experiments in science. Apparently, it's disrespectful, and presumptively wrong.
This is why we can't have social science. Not because the subject is not amenable to the scientific method -- it obviously is. People are conducting controlled experiments and other people are attempting to replicate the results. So far, so good. Rather, the problem is that at least one celebrated authority in the field hates that, and would prefer much, much more deference to authority.