It's been over 75 years and The Great Dictator is still a great comedy.
Something a lot of people don't realize is that back then, Charlie Chaplin was seen as an annoying, preachy douche for bringing up politics at all, especially because militarism and nationalism (both things he spoke out against) were actually very popular in the USA at the time.
The Great Dictator as a movie was popular because America was at war with Germany, and of course loved to laugh at their enemies. Audiences in the 1940's absolutely hated his ending speech though, they didn't want to be preached at and told that war was bad, that they needed to be good to others and be peaceful. What today is almost universally regarded as an inspirational speech in a time of the worst war in history, at the time was regarded as something extremely controversial and that could even potentially ruin Chaplin's career.
There's nothing controversial about making fun of Donald Trump. There's nothing controversial about "hurr libtards", either. Political comics and comedians today are just preaching to their respective choirs. Political comedy today is safe, and without balls, because nobody wants their audience to get mad at them, they just want to tell them more of what they want to hear because they're just doing it for a paycheck, and not out of conviction.