There's other solutions that can also be explored.

Where I am in BC, Canada, pharmacists can prescribe specific medications for certain pre-approved conditions, and there is also the concept of an "emergency" refill for if you lose your medication or are unable to get an appointment in time, a few days of a previously prescribed medication can be provided.

At the end of the day, a better solution is to have tiers of prescription meds. Not everything needs to be gate-kept by MDs. If an AI can prescribe it, there is no reason a nurse, pharmacist or other medical professional shouldn't be able to as well.