Sometimes I think that there is a lot of exaggeration around the story and scale of influence of the Ulster-Scots in America. However maybe many of the claims are justified, and it's our modern-day cynicism, and what CS Lewis called chronological snobbery which makes us question.
"... But the position of the Scotch-Irish in the New World was peculiar.
They alone, of the various races in America were present in sufficient numbers in all of the colonies to make their influence count; and they alone of all the races had one uniform religion; had experienced together the persecutions by State and Church which had deprived them at home of their civil and religious liberties; and were the common heirs to those principles of freedom and democracy which had been developed in Scotland as nowhere else.
At the time of the American Revolution, there were nearly seventy communities of the Scotch and Scotch-Irish in New England, including Maine, New Hampshire, Vermont, Massachusetts, and Connecticut ; from thirty to forty in New York; fifty to sixty in New Jersey; over one hundred and thirty in Pennsylvania and Delaware; more than a hundred in Virginia, Maryland, and Eastern Tennessee; upwards of fifty in North Carolina ; and about seventy in South Carolina and Georgia : in all, above five hundred settlements (exclusive of the English Presbyterian congregations in New York and New Jersey), scattered over practically all the American colonies..."
– Charles Hanna, The Scotch-Irish; or, The Scot in North Britain, north Ireland, and North America, (1902)