You have to fix the hypotheses to test before you begin the experiment, as otherwise you will stumble upon a lot of spurious correlations. That your birthday is the same day than someone's in your class/work group is a rare event, that two people have the same birthday in your class/work group, not at all uncommon. This is the birthday paradox. In the same spirit, with a drug you'll always find groups where it works because of spurious correlations, specially if you don't fix beforehand the group where you want to test it.
Run one trial to find correlations with specific groups, then run another trial under the hypothesis that it works for that group.
Well sure but that costs a fortune. Drug development is already extremely expensive.
That is a good idea, but it generates accusations of special pleading. Medical science is plagued with many kinds of fetish, and medical doctors are not generally obliged to actually understand science.
Such a drug should be approved but with a big warning that it only works in some cases.