Why is this film so good?

I can't speak for other people. I will say this though. Modern Times is still, to this very day, quite a modern film. One that tries to do more than entertain, but also use comedy to contextualize some of Chaplin's fears for the future ahead. And how that has been humanity's struggle throughout ages; merely to survive the oppression. Whether you're a spunky young girl, or a clumsy old tramp. You have to keep going.

It's a film with a message, but it's your job to figure out whether it's too heavy handed or not. I happen to think that because he uses the tramp it's the perfect balance of comedy and a sociological deconstruction.

It's the death of silent film by one of the architects of the genre while he was still in the prime of his career. A perfect conclusion to the tramp in cinema and a proper hint at the social satire he would go whole hog in for the great dictator.

Plus, it's still quite funny.
When that halfwit says goodbye to her husband and twinkles back into her house all happy, and then Chaplin totally makes fun of how stupid she looks, I die laughing. It's my favorite moment from all his films. the kind of moment you'd find in a Woody Allen movie.
It's a comedy! You'll laugh.

And at the end of the day, if you don't fall in love with Paulette Goddard, then there is something wrong with you.