Not sure I agree. Yes, of course they go with FDA they are only treatments with lots of studies proving they work. Most people with coverage and the money for the drug probably visit the doctor sometimes. Im sure they would mention or even be asked why they stopped taking it.
Doctors are the mechanics they are there everyday in the trenches. They see many many patients that use the drug at yearly checkups. They are aware of real world results even if its just a small sample of total population.
It goes without saying drugs effect different people differently so they will never completely safe for everyone.