It didn't create a perfect country for women, who were second class citizens for much of the country's history. It didn't create a perfect country for minorities who felt the harm of discrimination. But it made the country a heck of a lot better than it might otherwise have been, and it made a country that good people around the world wanted to migrate to, which in turn made the country better.
Yes, american exceptionalism has always been part myth, but I don't think the solution is to teach the opposite. Teaching that we are a country filled with discriminating nazi thugs has the same effect, just in the opposite direction. As a country we have tended to live down to that "ideal" as well.