>In the US, new houses are much larger than houses built in previous generations

If they sold those house to people of childbearing age, preferably earlier childbearing age, they would drastically increase the birth rate, but they don't. They only sell such house to people later in their careers who are out of, or at the very end of their child bearing years.

Of the people I know who have kids many of them are raising them in one-bedroom apartments the way our grandparents grew up. Talk about ways to ensure one and done.

>Plus we've allowed homeowners to restrict the building of density to protect their equity value.

This is highly effective way to suppress the birth rate. Don't create new living space, and people won't reproduce.