Parents are also allowed to restrict their children access to alcohol and cigarettes, but it seems a government ban on them buying those things works better

Given the ease with which kids who want them can get any of those things in schools, it's not clear that the government ban is actually doing anything of significance or that the reduction in usage isn't more a result of convincing people that those things are actually bad for them so they choose not to partake despite the continued widespread availability.

Notice that consumption of those things is also down for adults even though adults are not banned from getting them.

Doesn't seem to be a universal truth to me. As a teenager I had rather easy access to both cigarettes and alcohol in spite of usual age-restrictions legally imposed. I didn't care what gov't thinks about it. I did care about what my parents would do if I caught drunk though. That was my real barrier.

I’m sorry in what world is age restriction effective at keeping teens away from alcohol? Are you from the 60s?