If the FDA never got established, would firms emerge that put their seals of approval on medicine and become trusted? We will never know. It's pointless to point out what happened before the FDA and after because these are not random samples, the FDA didn't get randomly created. The demand for the FDA if denied would have transformed into the demand for something else.

We will also never know the progress in medicine we lost due to the red tape. There would of certainly been scandals and deaths, but if we got a cancer cure as a result would it not have been worth it?

I suspect that if regulation was not a feature of government we would of solved it in other ways, such as the ability to pierce the corporate veil both civilly and criminally for gross negligence etc. And third parties whose only product is trust - these parties would have infinitely more incentive to preserve that trust than governments.