Puritanism starts to lose its force as a stable form of religion in the colonies, not just because of the witch trials, but because the individuals in the colonies begin to establish independent secular lives that they do not want governed by the church or the theology of Puritanism.
That is why the Great Awakening occurs in the early 18th century, to remind people to return to the depth of faith that they once held. It is to remind people that they have become too secular, outside of religion.
Did Puritanism end? I don't think so. We just call it something else nowadays. There is still a Congregationalist Church, which is what the Puritans called their church. There are still legalistic groups, such as Seventh-Day Adventists or Assemblies of God or Churches of God, that have strict rules for their members. I grew up in such a church that didn't allow women to cut their hair or wear pants or makeup or jewelry, and no one could go to movies or dances.
The witch trials put an end to witch hunts, not to legalistic religion.