As it is, the only medications that require a prescription to buy in Saudi are psychotropic ones, narcotics, and most recently, antibiotics. Things like insulin, birth control medications, hypertension medications, even antidepressants and anti-psychotics- they are all OTC. And I think they should remain so, because from what I've seen the damage from misusing those drugs against pharmacists' advice is far less than the damage from going without them due to the difficulties encountered in seeing a doctor.
The reason that this is the norm here is twofold; one, health insurance wasn't much of a thing here until a few years ago. The second reason (and the reason health insurance didn't factor in until recently) is that the socialized healthcare system here was (and still is) stretched thin; seeing a doctor to get prescriptions for every little thing becomes prohibitively difficult, with appointments taking months.
It's asinine to expect someone suffering from, say, an acute athsma attack to try to navigate ERs or try to see a doctor on short notice during a crisis, when a pharmacist would be able to dispense the exact medication needed, leaving the others free for more complex cases that need closer attention.
Edit: this actually created a bit of culture shock for an older friend of mine. He was traveling to an EU country for the first time and didn't do his homework- he thought he he could simply walk into any pharmacy and ask for a pack of his cholesterol medication, as he usually does back home. I don't envy the poor pharmacist that had to keep trying to explain the dispensing system to him and to emphasize that yes, they are aware that it's Lipitor, not morphine, it's just how the regulation is.