Can you point out the enumerated power that the States gave to the national government to assume that role?
The FDA has its power to regulate consumer products under two provisions of the Constitution: the general welfare clause (since product safety is directly related to well-being, in that a product defect should not disable, poison, kill, or otherwise harm a person).
Article I, section 8 of the U. S. Constitution grants Congress the power to "lay and collect Taxes, Duties, Imposts, and Excises, to pay the Debts and provide for the common defense and general Welfare of the United States."
...and the commerce clause, since very few products are produced and consumed within a single state and no other.
Article I, Section 8, Clause 3 states that the United States Congress shall have power "To regulate Commerce with foreign Nations, and among the several States, and with the Indian Tribes."
I think that many, if not most, states have product regulatory agencies. All that would happen if the FDA were disbanded as some people advocate is that each state would then regulate each product separately, leading to a plethora of regulations, many of them contradictory and incompatible with each other. The costs of complying with 50 different regulatory systems would cause product prices to skyrocket for any industry that wanted to sell its product across state lines.
Note that none of the Constitutional authority for the FDA to perform regulatory functions according to its charter apply to use of the FDA to try to control behavior. For instance, the FDA can tell a soda company that its product must adhere to certain safety standards, but it cannot control consumer use of the product. It is your choice, as a consumer, to consume that soda. It is the FDA's job to ensure that it is made from clean water and not contaminated with bacteria.