Can't find it online, as it was published in the 80s, but Scientific American reported on a study where people were allowed to self-administer morphine whenever they wanted it. They were all in a hospital setting. The first finding was that there was enormous individual variation--some people took so little that the researchers wondered how it could have had any effect, and others took what they thought would be enough to stun a horse. The second finding was that pain relief was far more effective, because the patients didn't have to wait until they were really hurting in order to get access to morphine.
Thirdly, only 2 or 3 of the research population developed addictions--and every one of them had a prior history of addiction.
So yes, aggressive pain relief will produce more addicts strictly from a statistical standpoint, but so what? The answer to that is to know your patients in advance, and make sure that those prone to addiction get extra attention to make sure they are weaned off it before being released. They shouldn't get prescriptions until they agree to be hospitalized so they can be monitored.