Chair of FDA doesn't think prescriptions should be required for medicine

[haele]

19. A prescription if nothing else is a record.

So the pharmacist at least (And other doctors if there's electronic records sharing in your region) can tell what you're taking, if there might be any damaging interactions between dosages or drugs, and what potential risks you might need to look for if you use that drug.
Not to mention reducing the risks of over procurement of "medicine" for secondary sales, overdose, or illicit purposes which can reduce the supply of medicine for legitimate purposes.