We already have more than enough data about what happens in the absence of the FDA and its non-American equivalents. It's abundantly clear from pre-20th century history. The absence of government standards and inspection for food and beverages didn't give rise to competing private agencies safeguarding public health but with lower costs and more vigilance. It made fraud so easy and pervasive that some commodities were adulterated more often than not. Even when they weren't committing outright fraud, the absence of regulation made it regular practice for manufacturers to use compounds of arsenic, lead, and mercury as food colorants and additives. It wasn't that nobody knew eating lead was bad for you, or that nobody knew many commercial beverages and foods were tainted. The oldest reference to such problems I can quickly find on Google Books is from 1758, in
Elements of the theory and practice of chymistry by Pierre Joseph Macquer and Andrew Reid:
The Salt of Lead hath a saccharine taste, which hath procured it the name also of Sugar of Lead. For this reason when Wine begins to turn sour, the sure way to cure it of that disagreeable taste is to substitute a sweet one which is not disagreeable, to the taste, by mixing therewith Litharge or some such preparation of Lead: for the Acid of the Wine dissolves the Lead, and therewith forms a Sugar of Lead, which remains mixed with the Wine, and hath a taste which, joined with that of the Wine, is not unpleasant. But, as Lead is one of the most dangerous poisons we know, this method ought never to be practised; and whoever ever uses such a pernicious drug deserves to be most severely punished. Yet some thing very like this happens every day, and must needs have very bad consequences...
All the retailers of Wine have a custom of filling their bottles on a counter covered with Lead, having a hole in the middle, into which a Leaden pipe is soldered. The Wine which they spill on the counter, in filling the bottles, runs through this pipe into a Leaden vessel below. In that it usually stands the whole day, or perhaps several days; after which it is taken out of the Leaden vessel, and mixed with other Wine, or put into the bottle of some petty customer. But, alas for the man to whose lot such Wine falls! He must feel the most fatal effects from it; and the danger to which he is exposed is so much the greater, the longer the Wine hath stood in the Leaden vessel, and thereby acquired a more noxious quality. We daily see cruel distempers, among the common people, occasioned by such causes, which are not sufficiently attended to.
In an environment with much less government control, the poor customer got the most poisonous wine. The poor customer also had the least leverage to demand pure food and drink, to contract private analytical services if he suspected the quality of a product, or to get restitution if a product was indeed unsafe.
This and other dangerous and/or fraudulent practices were not greatly curbed in Britain and the US until another ~150 years passed, when governments established and enforced standards for food and beverage purity, safety, and labeling.