Turning the Nazis into a comedy trope was something that predated WW2. There were people who actively mocked the Nazis because they thought their pomp and rallies were ridicules.

Post-WW2 they received more humanizing depictions than the Soviets ever had. The comedy trope as you mentioned didn't really start until the 1960s with Hogan's Heroes that portrayed the Nazis as utter buffoons. The Producers was made by Mel Brooks, who made it his life's mission to turn Hitler into a figure of mockery and ridicule.

The reason why he did that is because he believed that by making Hitler look like the ultimate comedic jackass, no one would ever take Hitler and his ideology seriously ever again. He did have a point. His satires of Hitler were never co-opted by Nazis, who frequently co-op anti-Nazi satire and propaganda as their own (look at American History X. It is a serious critique of white supremacy, but the protagonist's handsome and muscular appearance and his attitude turned him into a Neo-Nazi icon).

The main issue is that people don't understand why Hitler was evil, why Hitler was dumb, and more over... how similar Hitler was to many other third-world dictators and tyrants that we condemn without a second thought. It was that he inherited the German state, which was far more advanced technologically and economically than other countries and thus actually stood a chance at doing the crazy shit they set out to do.

Mussolini had wide ambitions, but they were not targetted at Western European powers, and also he seriously lacked the capabilities of carrying out his ambitions (his attempt at wooing the Muslim world over to his side failed in a comical fashion). This is why Mussolini is often remembered as a goofball idiot and not the tyrant that he actually was towards his fellow Italians. Mussolini's family was not tarnished by his misdeeds and have been active in Italian politics. His great-grandchildren hold office and are still running and no one seems to care much for it there.

It was also very well-known that when fascism comes to American it will not resemble the Nazis in Nazi Germany. Sinclair Lewis noted that in his 1935 novel It Can't Happen Here that fascism will come in an American guise. HE is misquoted as saying that it will come carrying a cross and wrapped in an American flag. He didn't say that, but he definitely meant it.

The same thing is going on in Germany, with the AfD rising in power and might even be able to take office. It won't be like Germany in the 1930s and 40s, but it will be a Neo-Nazi state.