A comment is too short to summarize the reasons why, but I would refer interested people to Eliezer Yudkowsky's Inadequate Equilibria ― there is a 50 page dialogue between two humans and an alien visitor on the FDA.
It seems more accurate to say it does both simultaneously, or that it mis-regulates.
It fails to regulate some things that it should have (such as this), and it regulates other things that are better left alone.
And we should expect any noisy estimator to do that in general: there are always going to be both false positives and false negatives.
One thing we should be careful about though is to distinguish between arguments over the relative propensity of either, vs. the relative weighting that should be given to each.
E.g. sometimes people say 'no, the FDA over-regulates rather than under-regulates', when what they really mean is that the find that specific instances of over-regulation to be very harmful, while they think that the examples of under-regulation can be ignored.
I STRONGLY disagree. The FDA is underfunded and only looks into a tiny minority of cases deemed worth their effort. Walk into a "health" food store and look at how many unregulated drugs are on the shelf. They put out fires more often than they prevent them.
It appears to be another in a long line of entries in the "undergraduate economics solves all the world's problems" genre.
I would recommend caution in using Yudkowsky's long-form fictional strawmen to do anything other than analyze his own cognitive biases.
In general, the FDA under-regulates dramatically.