You make a good point, and at least personally when I am solely showing that a universal statement is untrue, I will take pains to explain that I do not view a single counterexample as representative of the typical state of affairs (just a disproof of the universal statement).

On the other hand, if one views something as a debate, with lots of back-and-forth, I think just pointing out the counterexample is fine--it's not an exchange of insults but an invitation to drop the extreme position and start talking about a more nuanced position. So I don't view it quite as negatively as you do.

However, I generally avoid doing it myself (sans sufficient caveats) because I prefer to model the nuanced approach that I would like to see.