I tried to show that that Coca Cola is an "exception" that proves the rule. With medications, people are really after the formula. If there's something preventing access to the source materials, like in Coca Cola, going after that particular formula isn't good either, as you won't be able to do much with it even after finding it out.

My contention with your position on patents is that, although they make companies publish the recipe, while in effect, they not only keep the formulas secret in practice, but also create a monopoly, preventing reverse engineering altogether. If you cut the duration of patents, the incentives of releasing as patents goes down as well, increasing the push for trade secrets. In the end, I posit that cutting the duration of patents will have similar practical effects to removing patents altogether.

Finally, I think your contention is exaggerated. Unless the drug is very niche, there's going to be a significant demand for them. This demand creates an incentive for better reverse engineering efforts. Patents make them illegal, almost nullifying this.