Homeopathic products are governed by the same law as are other drugs per 21 USC 321(g)(1)(A) “articles recognized in the official USP, official Homoeopathic Pharmacopoeia of the United States or National Formulary, or any supplement.”.

Supplement here is not referring to dietary supplements, but supplements to the respective Pharmacopoeiae.

FDA could not with a broad stroke or regulation just take away homeopathic therapies without Congress first repealing this part of US Code.

Back in the 1930's when the FD&C Act was being debated/discussed homeopathic health providers prevailed on Congress to make certain that the emerging drug industry at that time would not de-legitimize homeopathic treatments.

A number of Congressmen at the time were under such providers' care taking homeopathic preparations, and they swore by them. A provision was made for homeopathics in law then, and it still exists in law today.