I don't think the story is about Puritanism; it's a coming of age story for a young man who, despite being supported and sheltered by his "faith/Faith" for years, must journey into the world of imperfection/sin. After all, we are never sure that anything in the story happened, other than the fact that he entered the forest one evening and work up there in the morning. The story is about how he reacts to what he thinks he knows about the people of his village. He finds out that they are not as perfect as he always thought they were (or so it seems IF it weren't all a dream), and is destroyed by their failure to live up to his ideal of them.
I think Brown would have been destroyed by this "knowledge" in a Puritan society or any society.
"The enemy of the good is the perfect."
"Young Goodman Brown" casts the Puritan society in a negative light. This is best seen in Hawthorne's critique of hypocrisy evident in Salem. While the Puritans were incredibly hard working and resilient, they were deeply religious and viewed people as either elect (destined for heaven) or damned (destined for hell). It appears that there was little one could do to move from one category to the other. This, of course, would naturally lead to a great division in society. Those who were elect would naturally view themselves as superior to those who were damned.
Hawthorne criticizes this because it is ripe for hypocrisy. Notice how Brown views himself as elect, yet he allows the devil to lure him deeper and deeper into the forest. In fact, when he realizes Faith is in the woods, Brown becomes so enraged that he becomes the most frightening thing in the entire woods - including the devil and the black mass!
Notice too how the devil tells Brown those around him - and even his ancestors - were not as pious as he thought. He realizes prominent members of his own church are devil worshippers. He realizes his father and grandfather also knew the devil and received his help.
It seems that Hawthorne, who had an ancestor who served as a judge on the infamous Salem witch trials, criticizes the Puritans for neglecting to realize that all humans are susceptible to sin, not exempt from it.