The prescription is probably good for some limited number of refills.
The above mentioned case of doctors who require a pap smear for birth control is unrelated; it’s a barrier to access to contraceptives, which is motivated not by medical concerns or even greed, but by politics.
Things are probably different if this is a long term doctor you've established a relationship with; but in my experience no lab tests were done, just a lot of unnecessary paperwork and pay the lady at desk.