Ok but that's a democracy...
Saying the United States is a constitutional republic and not a democracy is like saying helium is a noble gas, not an element. They are both. One is just a subset of another.
Democracy has, for hundreds of years, had a general definition of "a system of government where the people can choose their governing legislation." The United States (and every free country) fits neatly into that. Even Wikipedia lists the United States republic as a variant of democracy. It isn't a direct democracy, sure (nothing is really) but a democracy it surely is.
I dunno. Seems the founding fathers or whoever were using the word "democracy" wrong.
In a "pure" democracy, everything would be done by referendum or the will of the "mob"; the governments of America and other 1st world countries which were inspired by it (e.x. Britain and the Commonwealth nations) didn't want "mob rule" or direct democracy, they wanted Representatives, Judges, and formal legislation deciding the country for the "people" - the only role the people were ever intended to play was in choosing the elected representatives, filing constitutional lawsuits, and so forth.
(Even ancient "democracy" which was its inspiration was limited only to aristocracts; slaves and women couldn't participate directly; today elected representatives, judges, etc may not "inherit" their power, as in old, aristorcratic forms of government, but they tend to be more educated, articulate, intelligent, etc than the "general public" or mob, and family, of course still does play an indirect role in it.).
An actual "direct democracy" would be like Escape from New York; basically anarchy or pure mob rule, the worst form of government there allegedly is alongside tyranny. The fact that someone with an IQ of 61 or a literacy level barely above the 6th grade lever (which 99% of mass, short-form media is marketed to) can participate in voting for our president and representatives is enough of a problem as it is (which is one of the main reasons that the Democratic party, more specifically, is even able to stay in business to begin with; by being effectively the party of the "illiterate" vote and trying to get people into the polls who can barely even fill out a job application).
Let alone a "system" in which they could decide everything by pure "referendum or mob whims".