It may never be cheap, but it should be possible to drive down the cost of housing to the cost of construction. A big part of getting lots of building done is to take a chainsaw to existing regulation.

* No minimum lot size

* No parking space requirements

* No single family zoning in the city - minimum is multi-family, 15 stories.

* No requirement to match the character of the neighborhood

* No height based additional setbacks

* No rent control

* Get rid of the anti-dorm laws[1]

* No historical preservation without the city buying the property in question

* No building plan for the city - replace it with a "shall issue" policy where the city has to have some affirmative reason to block the permit or it gets issued by default.

There's probably a bunch more that should probably be done away with; those are the ones I can think of off the top of my head.

---

1. It's very common in cities to ban dwellings that house more than x (typically 4) un-related adults.