You're both making points for why something being illegal could cause people to want it more, although I disagree with some of them. But that's not the point. I'm asking why we know that countries with drug problems and drug laws have drug problems because of the laws, and not drug laws because of the problems. Either is plausible. Of course, that's assuming that there aren't cultures with free drug use where it's a problem, or cultures where drugs are illegal and not much of a problem either, which I doubt.
I hesitate to say it because surely someone else already has, but the main reason is that under a black market, prices are
substantially higher than they would be under a legal market. For example, you can get a pound of loose tobacco for less than 20 dollars. Meanwhile, a pound of marijuana--despite the fact that criminal penalties for it are low compared to many drugs, and despite the fact that the plant is easy to grow, certainly easier than tobacco--will cost something like 1500 dollars at the very least, and can easily be 2-3 times that for higher quality.
This creates problems for two reasons. One, there are huge profits to be made in trafficking, profits which many are willing to use violence to protect. Two, the cost for the user is high, making it far more likely for them to commit crimes to "feed their habit."
A secondary problem is that a black market product can have dangerous additives, and be of inconsistent and unknown quality. It's a lot easier for a person to fall victim to an overdose if they don't, and short of relatively advanced testing techniques, can't, know how much of the drug they're actually taking.
A third possibility is that the availability of safer alternatives in a given class of drugs will decrease demand for the more harmful ones. For example, it's possible that if people could get amphetamines without getting diagnosed with "ADHD" they would be less likely to seek out methamphetamines. This one is pure conjecture, there's not really any available data on it, but I think there's a certain logic to it (particularly if we were in a situation where most drugs were legal but a few particularly harmful ones were not).
Keep in mind that some of the most inherently dangerous and brain damaging intoxicants out there are already totally legal--inhalants like glue and paint. Inhalant abuse is a problem, true, but it's hardly rocking the foundations of society.