There's half a kernel of truth in the diagnosis of the problem. Governments have caused a housing shortage, but not just the local cities.
* Federal environmental regs restrict building and are used by local activists to impede and stop building.
* State environmental regs do much the same, and many states' labor laws increase the costs of building.
* Cities use zoning to restrict building and tack on fees and take-aways, basically milking cash developers as if they were cows. "Use permits" are also used against developers, businesses, and churches (re churches, multiple cities have tried this to prevent any further building of churches in their city - they've been slapped down in court, but keep trying, forcing religious people to waste large amounts of $$ in litigation that should never have been necessary).
* Within states, but regionally, there are quasi-governmental and governmental creatures like "open space districts" that make large amounts of land off-limits for building or like CA's Coastal Commission that has such absolute power in "coastal" areas that they can refuse to permit a home owner to repair damage due to weather and age, unless the home owner gives up some part of their land or gives up some sort of "public access" easement.