In pretty much all countries that instituted heavy restrictions on smoking, e.g. banning smoking from restaurants, you can see an accelerated drop in number of smokers the years after that ban regardless of changes in education. This is particularly easy to verify because it has been done in many countries but all at fairly different points in time. Some did it decades ago, some have done it recently, there are still countries where it's allowed.

Forbidding things works very well most of the time. There are exceptions, but as a rule, it works.