If you remove arbitrary limits like density(height) limits and requirement for parking spaces, and lower the minimum space requirements, then the same amount of construction costs can have much more small "housing units" that each would be much cheaper than now.

Another option that has been used elsewhere is 'dormitory-style' housing, where the residents have their own small rooms but shared communal dining/cooking/shower areas; it has it's own set of problems but it is much more affordable; for people who can't afford better living space it's much better than living on the street.