Of course they do. They regulate airlines and all facets of their business. They don't have specific regulations for FF programs but all their rules apply whether you pay for a ticket with miles or with money.

From https://www.transportation.gov/indiv...lyer-programs:

While the U.S. Department of Transportation does not have rules governing airline frequent flyer programs, DOT has the authority to investigate unfair or deceptive practices in air transportation, including complaints from consumers regarding airlines’ frequent flyer programs.

Certainly selling a first class ticket on a flight (and an airline) where first class does not exist is unfair and deceptive.