Stereotypes are there because people are dense and are, mischievously, if I'm understanding correctly, looking to apply simple labels?
That is factually incorrect. Stereotypes are nothing more than mental shortcuts. Stereotypes die off as their predictive powers prove no longer usefully accurate.
Yeah, you can always find the exception. But that's just silly. Stereotypes are not based on the exceptions, they are based on the general rules of thumb.