We're not confused about why we do it. We're aware that doing it has negative outcomes.
No amount of prolix explanation excuses even the act of stereotyping.
It may be impossible to avoid stereotyping entirely which is why people practice not doing it. You call this "politically correct". I call it "behaving decently".
What in the hell are you on about. There is no one choosing to be homeless in LA who can afford a house in bumblefuck.
Per your other point there is nothing about the US housing market that is subject to natural supply and demand. It's a perverted tapestry of incumbents doing whatever they can to keep as many people priced out as possible.