If 8 families want to live in a single family home, it must be an exceptionally desirable area, with very little housing.

It stands to reason there are probably many more people who want to move in to the area, but who aren't willing to be one of 8 families in a single family home.

So given the huge amount of pent-up demand, there must be some building laws in place keeping this specific city from growing upwards, and generating supply for this demand.

This is probably a building limits problem.

There are plenty of places where land is cheap but units are still too expensive for low wage workers and their nonworking children.