Land supply in desirable locations cannot be increased; you can zone for increased density in those locations, but developers are not incentivised to release new supply as quickly as possible (as that would reduce prices). See for example https://www.fresheconomicthinking.com/p/a-housing-supply-abs... and other articles on that blog which explain this phenomenon.

The property market has too many inherent and imposed monopoly conditions that prevent it from acting as a hypothetical free market where supply and demand are the only factors that influence price.

Actors not motivated by profit can increase supply faster than the private sector's preferred absorption rate (e.g. mass state housing projects like in Singapore and Vienna), in which case sure, if the government massively increases supply consistently above demand and only rents or sells in a manner preventing monopoly acquisition then prices (rents or purchases prices) can be pushed down. There are other alternatives (e.g. Georgist style land taxes combined with liberal zoning laws, so efficient use of desirable locations is encouraged and enabled).