Why is there no multilevel parking? All that space can't be cheap. Is there zoning laws against it?
It is, and it's why dense housing can't compete. Cars are cheap, fuel is cheap, land is cheap. In the short term, other costs, such as harm to walkability, lack of community, pollution, etc are not quantifiable or too far out in the long term to make it a viable business proposition to go with density.
It wont work for high-rise buildings of course, but for slightly-less-central blocks that are say 4 to 6 floors, each apartment gets a parking space.