You are missing the point. Houses for poor people are almost never built, instead poor people live in 50 year old places that were built for the rich or middle class.

What happens is that 10 people move into those new places and 10 people move into their old one and the vacancy works it's way down the line. Eventually some guy down the bottom gets slightly cheaper rent or a better place.

Imagine that instead 100,000 high-end apartments were built in the Bay Area. None of them will have poor people move into them but instead places like (to quote elsewhere in the thread) "downtown PA (university Ave) its right around $2800-3000 for a 1 bedroom, for places with 20 year old appliances and no upgrades." might now be $1000/month cheaper and affordable by somebody on a lot lower income.