Um, Puritanism is the State Religion in the USA. They offer platitudes about separation of Church and State, but all the evidence points in the other direction.
If drugs were illegal in the U.S. merely for puritanical reasons, why would they also be illegal in places like China, North Korea or Vietnam? The religion they all have in common is statism.
The reason for outlawing them is simple: You belong to the state, and if you're taking illegal drugs, you're not being a productive member of society. If you're selling illegal drugs, you're not contributing to the welfare of the state in the form of taxes. It all goes back to statism. Of course, most statists don't like to admit this.
Saying this as a pro-legalization Christian who also doesn't like puritanism/legalism/statism...