I dislike this word for the same reason I dislike the clumsy use of the term “ban,” so let me start out by saying that no, I would not want to see people punished and/or silenced for uttering the word “problematic.”
But I do dislike it. Intensely. I dislike how earnestly it’s used, often with a faint moue of regret. I dislike, most of all, the built-in presumption that everyone listening agrees with its application.
Few things anger those who use “problematic” more than someone saying, “Wait, what do you mean? Why is that author/book/movie/artist etc. ‘problematic?’” It frustrates them because “problematic” is most frequently invoked on the way to advocating the exclusion/silencing/shunning of any person or work dubbed “problematic.” Questioning its use means they have to stop and think, not only about why something has been deemed “problematic,” but whether or not silencing (or “banning”) that problematic person or work is the right thing to do. The joy of their righteous march forward has been interrupted.
They might — God forbid! — have to formulate an argument.
This can be dangerous. Question whether or not someone or something is “problematic” and you just might be deemed “problematic” too.
It is the current favored jargon of the censor.