The German defeat was also sped along both before and after US involvement by the diversion of resources to militarily unimportant goals such as manning the death camps.
A grotesque oversimplification..... the monstrous Holocaust damaged the German War effort in far more egregious ways than diverting the mostly second line troops who formed the Death Camp guards.
Despite Nazi lies to the contrary, large numbers of Jews had valiantly served in both Austrian and German Armies for centuries... these men were instead murdered.
War work was disrupted when skilled Jewish workers making everything from gun sights to uniforms were taken off the job and murdered. (This omits those who fled Germany ahead of the SS.)
The same thing happened over and over again in conquered areas in the East - Nazi overseers trying to get local production restarted found experts and workers had already been killed by the Einsatzgruppen...... yes, large parts of the Holocaust did not occur in "the death camps", but on the spot or in ghettoes all across the East. This slaughter, along with the partisan movement which arose in large part from Nazi genocidal practices, is what occupied,delayed and killed those first line German troops.