The problem is that herbalists are forced to go through trial and error to come up with this information (tradition just means that someone else already did), b

The problem is that herbalists are forced to go through trial and error to come up with this information (tradition just means that someone else already did), because they do not have a working model of how their herbs work. Modern medicine has a vastly better model of human biochemistry (although it obviously still has huge gaps), which allowed it to develop a ton of new drugs in a surprisingly short amount of time (around 100-150 years, which is nothing on the scale of human history). Regarding leeches and bloodletting, of course it helps in some cases, in the same way that executing random actions sometimes helps: by chance. To get from anecdata to systematic application, you need scientific inquiry to form a model of why it helps.