Yes, stronger laws on prescription medicines would reduce the rate of drug abuse overall, because it is far too easy for doctors to hand out meds like candy, and it is far too easy for those who receive them to redistribute them. Doctors who run clinics where they hand out scrips like candy need to be monitored.
Yes it would if you stopped the legal drug pushers from writing scripts so easily and cut off their ways to get kickbacks from the Pharmaceutical companies. They wouldn't be so quick to write that script, but when you make it so easy to make some extra cash from the Pharmaceutical companies the Legal Drug Pushers will push them even harder. There are natural ways to deal with the pain that a person may feel. I had 2 surgeries. My first one was on my Esophagus I had pain on my incisions in my abdomen. I asked for ice first and pain medication later. Then I had my gall bladder removed. I used ice on this primarily and it dulled the pain. If you can numb it and focus your mind on other things you don't need such harsh chemicals.
Stronger laws on prescription medicines would reduce the rate of drug abuse overall. Laws that would allow cross pharmacy databases which keep track of how many times a person has filled a certain prescription during a month would reduce the rate of drug abuse overall. Even though people can only be supplied a months supply of a controlled substance, there is nothing that is stopping people from seeing more than one doctor and having multiple prescriptions filled by different pharmacies.
People who want to abuse drugs will. If prescription drugs become harder to get people will just buy from street dealers they always have. Or people will abuse legal drugs that don't even require a prescription like alcohol or even a number of OTC drugs that can get you high.
Making it harder for legitimate patients to get treatment just so politicians can pat themselves on the back and act like they've actually done something useful is NOT going to help stop drug abuse.
Stronger laws on prescription medicines will not reduce the rate of drug abuse overall. It will make prescriptions harder to access for those that need them as well, which is not something we should be trying to do. Drug abuse does not require a prescription or a pharmaceutical product. You are not going to stop a drug abuser by changing the laws around a little bit. The only way to really stop an abuser is to attempt to get them medical care.