I see no existential, ethical, or legal problems with this. /SARCASM

If it can qualify as a practitioner, it should qualify fully as a practitioner, either as a physician who’s qualified to practice medicine or a nurse practitioner the same way.

Pragmatically I could see an AI performing as well as pharmacists who have limited prescription ability. However it would require a lot more holistic human interaction, which again gets into confidentiality and data privacy.