The Basic Law and the United Nations says housing is a human right. The problem with the market solving a constitutionally protected right is, in this case, that housing is expensive to build. For one thing, history shows that capital tends to build too few homes in order to increase rents as much as possible. Market rents are not a solution if we want even low- and middle-income earners to have good housing. We can afford to build good, beautiful and aesthetically varied rental properties with low rents for everyone with housing needs. Read more here.
Social Housing combines market rents with subsidized rents for the most vulnerable. This tends to be a costly solution. It increases stigmatization and class antagonisms. Why should the rich tenant be punished by paying higher rent? In addition, can it prevent the poorer tenant from switching to a better job? In that case, the poor risk losing their home. Furthermore, high rents reduce purchasing power. Low purchasing power reduces growth in society. When it becomes less attractive to acquire a rental property, the demand for privately owned homes becomes too great, which leads to hyperinflation of private homes and the consequent escalating private indebtedness.
A good housing market is based on the fact that you do not have market rents and that society keeps the rents. This is done by the state subsidizing the construction of good, cheap and beautiful rental properties for everyone who wants one. This does not have to be expensive, if the interest deductions for privately owned homes instead go to subsidize rental properties, then the demand for privately owned homes decreases. Then the prices of privately owned homes fall and the need for private indebtedness decreases. Read more here!
The state can also create money. It is a traditional part of social democratic politics that the state if new production is needed can create money.
About the importance of build beautifully.
KTH thesis shows that it is not more expensive to build beautifully.
You can also imagine that you are reviving an old model from the 20s: Municipal housing companies with the mission to build as much as possible, i.e. ignore the profit motive.
However, other planning instruments are needed than today. According to the Swedish Housing Agency, the most limiting factor for construction in the big cities - or at least it was during the 10th century - is the lack of urban-planned land. Nothing is planned until there is a construction company that wants something built. The forward ratio is zero. This differs from e.g. the end of the 1800th century when there were city plans, often larger than the already existing cities, with which it was just a matter of adding buildings.
So it was quick to build then too!