The FDA was established at a time when virtually the entire population of the US was literate [1]. While I don't have the heart to look up statistics, I suspect that the US at the time had the highest (or at least among the highest) newspaper penetration of any country, and that newspaper penetration would have been quite higher than today. Public libraries and schools would have been in full flourish too, by that time. My grandparents grew up on farms on the edges of the High Plains--where you would expect to find the most bumpkin of country bumpkins--and illiterate and ignorant they were not.
For someone whose argument is that the federal agency is necessary only because of public ignorance, you sure seem to be modelling that ignorance you think no longer exists. The problem with your argument is that you neglect to reason that both information and misinformation are incredibly easy to come by, and most people are unwilling or unable to differentiate between them.
[1] It is worth pointing out that, if you measure literacy by the ability to read in your native language, Western Europe has been majority literate for over a millennium.