re: How were German armored divisions so much more elite than their US counterparts

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Around the time of WWI - there was still horse cavalry, of course, but it was a clearly dying combat branch.

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Not so much. My great-grandfather was CG at Ft. Riley during WW2 and I have reams of his personal documents. In them are numerous references to the transition to mechanized cavalry and how rapid it was, but while rapid mechanization for the European theater was the main effort, non-mech cavalry was still needed in the Pacific theater where mechanized units were being out maneuvered by Japanese horse-drawn artillery. Simply couldn't cope with the mud and terrain on the islands. So there was parallel development of mechanized and non-mechanized cavalry from the replacement centers.