Your only looking at one side of the market equation. Landlords have to compete for tenants as well. They can't just raise rent to whatever they want, they all

Your only looking at one side of the market equation. Landlords have to compete for tenants as well. They can't just raise rent to whatever they want, they all compete with eachother. Only in markets that are severely supply constrained like the bay area where this wouldn't work. Also, in areas where new supply could easily be added, if more people have money, it will create new demand for housing and it will be built.