It also has to be said that at this stage of the war the Nazis had nothing to gain by crushing the uprising (nor expend resources in the process) and in fact politically much to gain by pulling back and letting the Poles declare a free government.
All true, but that wasn’t the perception of their insane leader.
True. But Hitler hated the Poles and wanted the country to be destroyed. After Jews were killed, the next target was the Poles.