Medicine is not like trying out a new coding framework - in some cases, like cancer:
i) There is no ability to "try it out for your self" - you are either all in or not
ii) There are extreme risks to taking the drug (most cancer drugs are actually somewhat to extreme toxic...just less toxic than cancer)
iii) You only get a few tries (since, you know, cancer will kill you).
iv) People are very desperate and will try anything
v) Data sharing is very very hard given the sensitivity of the information (patient data) - making it effectively impossible to have an open data exchange. (This is also due to the billions of dollars at stake on the pharma side).
Try designing a system to overcome those challenges...and you will likely end up with a central governing body that looks like the FDA. Anything else you are going to get way way more drugs that don't work, which waste time and money and kill people, which endanger patient privacy, or which are not satisfactory to pharma or, ...
The fact is, the FDA is full of many of the smartest and hardest working doctors and scientists in all of medicine. They take their jobs extremely seriously. They are far more careful and rigorous than most academic or even pharma-level researchers.
Do they get it wrong? Yes, occasionally. Not frequently. Occasionally. But that also, is science. The FDA follows rigorous statistical procedures, but even p<0.05 (or <0.001) still means false positives can happen.