Yeah, there's a lot of history to this, but it's a part of why there's so many unusual or distinctive off-shoots of Christianity that come from the US: Jehovah's Witnesses, LDS, Seventh Day Adventists, Evangelicalism, etc...

It's not just the Puritans, in fact, it's mostly not, though they've given us plenty of other cultural baggage.

Because we weren't our own nation, we didn't have our own bishop in the church of English, so for ministers to get ordained they had to go to England to be trained and then come back.

This gave rise to a conflict between the New Lights and Old Lights. The New Lights were basically proto-evangelicals and they determined that the proof of qualification to be a minister wasn't a degree, education, or some church approval from overseas, but the ability to gather a church.

This meant that charisma became the defining trait for a successful minister. They're not educated and they're terribly persuasive. This is why evangelicals have such terrible theology. There's all these ideas that are mainstream evangelical ideas that never existed before this period.

The rapture was created during this period. That's right, for nearly 1800 years Christians wouldn't even know what you meant if you said "the rapture" and now evangelicals wander around telling everyone to be prepared.