I think it might be interesting also to talk about the quality of housing. You touch on a related topic "making the city less desirable to residents", but I think it's worth adding something to that.
If you segment the housing by housing deemed good enough by people with high incomes, and housing of a quality which they won't live in, you can achieve the goal of allowing in lower income people without satisfying the demand for all of the higher income people (either high income people won't work and live in the city, or they'll commute from somewhere with housing they want).
Additionally, you can lower the threshold for people living in the city to live outside the city by making commutes easier.
This could also be used to demonstrate how replacing old and lower quality housing with luxury housing could negatively impact people with lower incomes, even if you're building more luxury units than there were previously low quality units, since in this thought experiment the market for luxury units doesn't affect that for low quality units (this refutes a commonly posed argument that it's good to build luxury housing as long as it's lots of units).
I can't say for certain that they market actually segments like this, but it's not too hard to convince yourself that it does.
I think it might be interesting also to talk about the quality of housing. You touch on a related topic "making the city less desirable to residents", but I think it's worth adding something to that.
If you segment the housing by housing deemed good enough by people with high incomes, and housing of a quality which they won't live in, you can achieve the goal of allowing in lower income people without satisfying the demand for all of the higher income people (either high income people won't work and live in the city, or they'll commute from somewhere with housing they want).
Additionally, you can lower the threshold for people living in the city to live outside the city by making commutes easier.
This could also be used to demonstrate how replacing old and lower quality housing with luxury housing could negatively impact people with lower incomes, even if you're building more luxury units than there were previously low quality units, since in this thought experiment the market for luxury units doesn't affect that for low quality units (this refutes a commonly posed argument that it's good to build luxury housing as long as it's lots of units).
I can't say for certain that they market actually segments like this, but it's not too hard to convince yourself that it does.