By the way, by this logic a Nazi hegemony would also have led to such rot decay

Of course, it would have. It happens to every civilization. The pace of ruin and collapse would have depended on who succeeded Hitler If Himmler succeeded him, there would've been some kind of civil war and North Koreanization of Europe over time. If Albert Speer or the Wehrmacht succeeded him, it might've existed for another 100 years but eventually, the same rot would afflict it as well. It happened to more hardcore societies like Rome and Sparta, it would've happened to them as well.

However, my belief is that if the Nazis won ww2 and conquered Russia, and subjugated Britain, it would've led to world-ending nuclear exchange down the line. The US would never accept peace and would arrange a permanent naval raiding policy against German shipping and as well occupy the middle east to deprive it of oil.

There might be some temporary truce by 1948, but eventually, both sides would hit each other with ICBMs. The US would initiate as its elite could never tolerate Nazism. It never happened in our timeline because the American elites had great sympathy for communism. Their view was that capitalism was a superior way to create the egalitarian, anti-racism, world hippy society. Communism was not the right way, but the commies had their hearts in the right place.

Against Nazis, they'd be fight to the death nuclear jihadis.