He appointed a cabinet of intellectual heavyweights including Andrew Mellon, Hoover, and Charles Evans Hughes. His appointment to the Supreme Court included William Howard Taft.
Yes....I know you will trot out Teapot Dome but, all things considered, it was vastly overrated in importance. Only one cabinet official was convicted. He was secretary of interior Albert Fall who was convicted on a single charge and aquitted on all others. Fall's recent biographer argues that he was mostly a scapecoat. The other corruption involved lower level people and was mostly piddling.
Harding was not personally involved in the corruption. When he found out the first inkling of evidence he shook one of the guilty parties by the lapel in anger. The corruption was trivial when compared to that tolerated my many "greats" such as FDR.
All it all...I'd rank him number one for the twentieth century.
BTW, most of your top ten became "great" by taking us to war. Is there a pattern here?
Nope, most of them were great by being great: The most recent example--Ronald Maximus Reagan!
Warren G., IMHO, was the "Clinton" of the 1920s. A total immoral failure!