Theyre in short supply because of artificial scarcity, which benefits the people who own and rent land. The government loosening building regulations would not fix the fact that it is more profitable to create artificial scarcity.

Also you're pretending like the government is in opposition to landlords. The leech class owns the government, that is why the term "dictatorship of the bourgeoisie" or alternatively "democracy of the bourgeoisie" was invented.