Sab,
I don't agree with your statement. In my spare time, I read a lot of American history and biographies. The Quakers certainly were the moral conscience of this country and exerted a profound influence on Pennsylvania. They always had minority status. It is clear that the New England Puritans and the Church of England/Episcopal were the primary denominations. We still have Puritan ideals of hard work and commitment. I believe the American character was forged by several factors. First, it took much courage to settle a wilderness. Ties with Engalnd remained strong but we were physically detached. England could not be bothered very much with America until they wanted to tax us. Society still had to function so, in great contrast to Ireland, Americans assumed they were English citizens, not subjects. Our colonial legislatures floruished. In practical terms, Americans governed America for a long time. Second, we had vast natural resources. The soil was so good, unlike the one crop depleted European soil. No one in America was poor, compared to the wretches in England and Europe. Third, since we viewed ourselves as English citizens, we took the rights in the British constitution very seriously. Third, we became a nation of immigrants from all over the world. The closed British/Dutch presence was disrupted by aliens. Altho a British/Dutch elite still exists, esp. in NY and Boston, we integrated practices and cultures from around the world.
Alexis de Tocqueville, a Frenchman touring America soon after the Revolution (Rebellion) described an American character that continues to this day. One meets a lot of Europeans doing business and touring Manhattan. They hate the American character but seem almost kooky in their love for regular Americans and our culture.
I used to attend Quaker meetings. Both in Britain and America they spearheaded the abolitionist movement. I saw them first hand in the civil rights and antiwar movements. They were more responsible than most. Their ethical development is impressive. They have not made much of an impact on our foreign policy, especially our wars. I don't know whether this is good or bad.
In sum, I feel they are the conscience of America, calling us to loftier ideals. Their Christianity is so compelling. They are our prophets. When I visited Occupy, they stood out b/c they had a commanding knowledge of the politcal process. They were not radical chic for the moment. They certainly had an influence but I don't think it was ever commanding or central.