The chief reason for exterminating the Jews was that the Nazis knew the war was over the second they waged it and embarked on a megalomaniac suicide waltz through Europe, raping the Jewish folk. The SS are the real winners of the War, since they got slaves and power before living a comfortable elderly age with Jew gold.
Jews were the perfect victim to the perfect rapist. That's why relations between Nazis and Zionists were so amicable, the Zionists weren't a good victim.
It's such a horrible, horrible thing. Plato's Republic which I am reading now is very interesting in this aspect.