Prohibition policies were not useful in any way in reducing the spread of addiction among gamblers, especially since gambling activity can be practiced on any game locally without the need at all for the presence of the state or one of its institutions to regulate.
You're right because if prohibition could have been the way out to solve every gambling addiction then those that would have first supported this are the governments, because they wouldn't want the people to be that involved in gambling, meanwhile that is not the problem about addiction in general, people also get addicted to other things aside gambling such as alcohol, food, women and other pleasurable things around us, so using prohibition policy is like stopping gambling itself all because of addiction which is impossible.
The most clear examples of all of this can be found if you succeed in finding statistics on gambling activities in countries whose laws completely prohibit the practice of these activities, and which are always countries that derive their laws from the Islamic system of positive rulings that clearly forbid gambling. The rates of gambling activities in these countries will be high compared to the laws that are supposed to prevent this. Of course, we will not hear about any cases of pathological addiction, and therefore we will not hear about any role that the state can play in that.