Are you sure they did? Maybe they were just OK with programs that didn't actually work.
What does work is restricted access through age limits, closing times, and higher prices (through taxes is what's been studied, but it's safe to say making something illegal also increases prices). These are unpopular policies, and those who profit from alcohol/gambling/etc. have an easy time mobilizing opposition to it.
What has been studied little, but was a big part of historical anti-alcohol movements until total prohibition won out, was profit bans. Government/municipal monopolies were justified in that it took away regular people's incentive to tempt their fellow citizens into ruin, and the idea was that while government may be corrupted by the profit incentive, at least they carried the costs of alcohol/gambling abuse as well. (Some teetotallers didn't think that was enough, and came up with rules that e.g restricting municipal monopolies from spending the profit as they pleased)