William, the distinction in that James Fenimore Cooper passage you quote between equality of rights and equality of condition (or as we might say, equality of opportunity and equality of outcomes) is certainly extremely important to keep in mind, but his assertion that “Equality is no where laid down as a governing principle of the institutions of the United States” does seem to ignore the Declaration of Independence, doesn’t it? The Declaration seems to lay down equality as more or less the first governing principle of the institutions of the United States:
We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable rights, that among these are life, liberty and the pursuit of happiness. That to secure these rights, governments are instituted among men, deriving their just powers from the consent of the governed.
Exactly what that means, and exactly how it might be expressed in governing institutions, is of course a long and complicated question, but it means something, doesn’t it?