What kind of actions are you considering that do not affect the market? Government housing affects the market by creating artificial supply. Regulations affect the market. just about anything that the government does will affect the market.
If you believe that housing is a basic right and everyone should be housed, then relying on supply and demand is not going to work. There's nothing inherent about a market that would house everyone, if anything, a market would reach an equilibrium where supply meets demand at some point where some people are not able to afford the supply and suppliers do not have an incentive/are unable to meet the price point of the remaining demand.
If you believe that housing is a basic right and everyone should be housed, then relying on supply and demand is not going to work. There's nothing inherent about a market that would house everyone, if anything, a market would reach an equilibrium where supply meets demand at some point where some people are not able to afford the supply and suppliers do not have an incentive/are unable to meet the price point of the remaining demand.