Um, not quite Alien. The Bill of Rights is the first ten amendments to the U.S Constitution, not the structural stuff about the Electoral College and so on, which is found in the Articles. The debates of the period, much of which feature in The Federalist Papers, consider electoral tyranny, among other things. Those first amendments were added to answer objections raised in those debates, in part by taking some things out of consideration for elected bodies ("Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof; or abridging the freedom of speech, or of the press; or the right of the people peaceably to assemble, and to petition the Government for a redress of grievances. " —First Amendment, U.S. Constitution, emphasis mine)
This seems to be a recurring problem in American history. Portions of the Fourteenth Amendment (specifically the Due Process Clause) apply most of the rights in the Bill of Rights to relations between citizens and state governments; the doctrine is called incorporation, and has come down as a result of SCOTUS rulings applying the Fourteenth Amendment (ratified in 1868) over many years. Even today, there are people who want to enact laws to strip citizenship from the American-born children of illegal immigrants (another unpopular minority), despite the specific definition of their citizenship in the Constitution. Some polling indicates that such measures enjoy majority support.
You are right to imply there is a difference between theory/the ideal and practice ("Actually what we got..."). Jim Crow laws in the South (and similar restrictions in other parts of the country) were enacted and enforced in the century following the Fourteenth Amendment's ratification. I also recall reading of people in North Carolina recently trying to oust a newly-elected atheist by applying a religious qualification for office in their state's constitution, despite incorporation and the explicit denial of religious tests for office in Article 6 of the Federal Constitution. You are also right to suggest that there was a notion prevalent in the Founding period that some citizens were better qualified than others; John Adams was a notable proponent of this idea, and it was at the heart of his political rivalry with Thomas Jefferson.
I can only answer Elkhound with a quotation from Winston Churchill: "It has been said that democracy is the worst form of government except all the others that have been tried." Put another way, good governance requires good people doing the governing.