First cities are not closed systems. Places like LA and the Bay Area have a built up demand that exceeds housing. The new housing would have to be added at an extremely high right to keep up with that demand otherwise the city just grows rather than becomes cheaper. When a city simply grows, the cheaper units never flow down to the bottom of the market as someone else will move in who lives outside the city and was previously priced out of the mid-tier housing. We see the same type of thing when designing transportation systems in a city. Adding in a new road can actually increase traffic as it ends up encouraging more people to drive who otherwise wouldn't have.
Also the housing market is not a singular market. The type of person who would live in a 3 bedroom luxury condo is not the same type of person who would live in an SRO hotel that shares a bathroom. Most people have a small window of what housing they consider acceptable and what budget they can afford. When a city gentrifies and knocks down SRO housing and replaces it with luxury condos (something that has happened a lot in both LA and the Bay Area over the last couple decades), the available units at the bottom of the market decreases in favor of the top of the market. That doesn't result in everyone in the city just moving up one rung on the housing ladder. Competition for the affordable units is now even higher because there are less of them available.