your assumption is that threatening mandatory compliance is better than voluntary compliance. Humans are irrational and sometimes resist doing the right thing when force them to. Surely you have had the experience that being forced to read a book for school has ruined it, or resisted doing something you wanted to do just because your parent made you do it. If instead you work harder to get assent and consent, your vaccination rate might be higher than if you threaten to hammer it in. Especially in a society where voluntary compliance and resistance to authority is in its social DNA, like the united states.