There are plenty of examples in NYC of forcing the developer to build infrastructure in order to get more building rights. In the suburbs developers are often required to build the underlying infrastructure for their subdivisions.

It's simple math. If the cost of building the development + required infrastructure is less than the price can sell it for then things will get built. It's the responsibility of the city to bundle the infrastructure requirements onto the building permit.

No, but they and their client certainly pay the property taxes and fees to make such things a possibility. More density = more property tax revenue = more facilities and infrastructure possible.