In any given area the amount of land is fixed, you might be able to slightly increase the supply with some land improvements like draining a marsh, but there's nothing that scales.
To house more people, you need to build denser housing on the fixed supply of land. Most places have zoning laws that limit density. But beyond that, it's actually less expensive to build higher cost homes - a lot of small apartments require a lot of walls (more material) redundant plumbing and electrical (more labor) and you need to handle the sale or rental to more parties (more overhead). If they do build apartments, it's going to be samll 1 and 2 bedroom apartments because those are lower risk - you'll always find some young people who need a place and can get a parent to cosign a lease and who will let their landlords treat them like crap. 3 or 4 bedroom apartments appropriate for families are harder to move, so even though those tenants might be able to pay proportionally higher, the opportunity cost of vacancies makes them a non-starter.
To house more people, you need to build denser housing on the fixed supply of land. Most places have zoning laws that limit density. But beyond that, it's actually less expensive to build higher cost homes - a lot of small apartments require a lot of walls (more material) redundant plumbing and electrical (more labor) and you need to handle the sale or rental to more parties (more overhead). If they do build apartments, it's going to be samll 1 and 2 bedroom apartments because those are lower risk - you'll always find some young people who need a place and can get a parent to cosign a lease and who will let their landlords treat them like crap. 3 or 4 bedroom apartments appropriate for families are harder to move, so even though those tenants might be able to pay proportionally higher, the opportunity cost of vacancies makes them a non-starter.