Can you suggest a similarly compact (doesn't even have to be one word, I'll settle for three or four words) I alternative that conveys similiar meaning?

The reason the term gained popularity overnight is that it fills a hole in the (informal) English language.

The phrase "Going Full Karen(TM)" in your post didn't add any information; it was just a gratuitous trope. Your comment says the same thing when that bit is deleted, and says it better. Therefore my suggestion for an alternative phrasing would be the empty string :)