More of course can be said, but we had an AMA with Dr. John Turner - /u/John_G_Turner - a few months back on his new book on the Mayflower which you may find of interest as he touches on this at a few points.

In addition, /u/anthropology_nerd has some excellent older responses, in particular this one, which I'd also point to, for analysis of why the Mayflower sits so prominently in the American mythos.