> We know they do because before the government took over the job, the nascent medicine industry would sell you literal poison.
We also know that some reports of poisoned industries in the past were exaggerated (and politically capitalized to lobby monopolistic regulations). This wasn't exclusive to medicine.
> The place where you can buy literal homeopathy sugar pills, and various completely unstudied compounds and other scams.
Presuming that these aren't actual cases of fraud - if they were, they'd already be illegal in a private market, regardless of the FDA - how many are actually buying these? Not many, I presume. For those that are, I think better informing them is much better solution, not only to combat innefective drugs, but also to strengthen trust on actually effective treatments. That said, homeopathy seems more like a yet-to-be cracked down case of fraud, regardless of regulations.
> If private industry was better than the government at managing drugs, the American supplements industry would mean we should have dramatically better health outcomes and dramatically cheaper healthcare.
Why? USA's healthcare system is an overly bureocratic, poorly regulated (not as in lacking in regulations, but that the regulations that exist are bad) goliath. It's closer to a government-funded system, except stupid. It's not an example of a government-free system, but how private actors do their best to exploit existing and lobbied soon-to-be regulations in their favor.