If the first experiment was wrong, the second experiment will end up wrong too.
...and now you have two problems X-)
Science should not go even slower than it already does
It's not a matter of speed, it's a matter of velocity. Going fast in the wrong direction is (much) worse than useless.
you are unlikely to hit statistically significance where there is no real result
You are quite likely. You start with a 5% chance under ideal circumstances and that chance only climbs from there. P-hacking is very widespread.
Instead, you irrationally do more screenings
8-0 You think getting additional screenings after testing positive for cancer is "irrational"??
The process of screening itself involves risks, not to mention the misplaced stress and possibility of unnecessary surgery.
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.