You're not really saying that the populous would finish more courses of over-the-counter antibiotics, are you? Prescriptionless antibiotics would almost axiomatically make that worse.
So then what's the fear? If they take antibiotics for a bacterial infection and don't finish it's same as the current state of the world. If they take antibiotics for a viral infection and don't finish them then no harm no foul if you believe the theory that this is how resistance occurs.
Hard to create a strain of antibiotic resistant bacteria when you didn't have any in your system to begin with. Turns out you can't #gatekeep #girlboss your way out of this and have to educate your way out regardless if antibiotics are behind-the-counter non-prescription or not.