But it is, that is the essence of a stereotype. If we take out the ethnicity factor and go into personalities your argument is the same as saying that it is embarrassing and damaging for Librarians to be labelled as boring and strict, for Managers to be labelled as conniving bastards and idiots, for Artists to be labelled as always high on drugs, for Nerds to be labelled as outcasts and acne ridden.
I consider your argument flawed in that stereotyping will always have an element of "there's some truth in your fiction and some fiction in your truth".
Fiction and Fact are two completely different things. It's a good thing many people appreciate fact.
> This is tantamount to saying "I have a right to perpetuate racially-based stereotypes, despite any claimed or real negative effect they have, because my ability to be funny depends on it."
Not just my ability but also that of the Film Industry, TV Productions, Stage Plays, Books, Music, which all continue to use any form of stereotyping for good or bad.