I don't know if it's because of this, but as a European I was flabbergasted the first time I went to a pharmacy in US with a prescription and they told me "come back in an hour". Like what? In Europe you talk to the pharmacist, give the presciption and 5 minutes later you're out.
That varies by location quite a bit. I can generally walk in my local pharmacy and have a prescription filled in a few minutes. Maybe more like 15 minutes if it's a controlled substance. But as a practical matter I just walk in, pay, and pick it up, my doctor sends the prescription over electronically. And lately, any recurring prescriptions are handled by mail anyway.
Have I ever experienced that "come back in an hour" phenomenon? You bet. Then I went to a different pharmacy.