There has never been a point where tipping point public demand for regulation did not lead to regulation (if it was for example unconstitutional to regulate). Which makes the assertion that regulation is the solution unprovable.
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.
You say regulation solving problems is unprovable when we have many examples of it doing so, then you claim that without regulation, we would solve things other ways, without any examples of that ever happening, let alone on a large scale. To “pierce the corporate veil both civilly and criminally” is legislation, as laws determine what is criminal. We also had exactly that in the US, where corporations lobbied for reduced regulation, saying that lawsuits would keep them honest through monetary losses. They then immediately went about lobbying to reduce lawsuit liability, cap payouts, and launched a vast PR campaign to paint lawsuits as money grabs by unscrupulous people looking for a payout.
And why wouldn’t a company “whose only product is trust” not be incentivized to sell that trust to the highest bidder? Companies sell out all the time and continue to do good business for a decade or more on customer trust they built up or came with the brand name they bought.
The saying “regulations are written in blood” comes to mind. So where are all the examples of things getting fixed through other means when regulation isn’t written to fix something?