Our drug stores kept regular hours. Never heard of middle of the night prescription. I was given meds in Emergency.
We had a couple of 24-hour pharmacies back in the Bay Area. If you ended up at an urgent care center late at night and needed a prescription filled, that’s where they sent you. A couple of the local Walgreens here in Central Texas are open until midnight.
We have one close to us that is 24 hrs. Have used it during an emergency a couple of times.
My daughter worked in a 24 hour pharmacy while going through school. They got business all night long.