If there's a distinction being made between "using AI for math" and "the particular methods being employed by OpenAI", I think that's splitting hairs. The core of the issue is that math is being done outside of people's heads by a different thinking system and they're worried about the implications.
If you look at something like the EPA (or the FDA as you mention), it is true that certain uses and side-effects of technology have been identified to be detrimental to society and have been restricted, but this letter doesn't seem to be in that league, it really seems like sour grapes to me. Dumping toxic chemicals into the water table is one thing, saying "we don't think people will learn from these methods in the same way that they traditionally have" doesn't hold as much water to me.