I suppose it might work like council housing (used to) work in the UK. The council builds large numbers of homes and houses people in them for lower than market rentals. Of course people are still free to build and buy homes privately if they want.
The problem with this in the UK was that the stock of council housing became immensely valuable and as soon as we had a right wing government they started to sell it off. Selling it off created home owners (who are more likely to vote for that government) and raised "free" money which could be given out in tax cuts, so it was a natural target.
In the UK an alternate system - housing associations (HA) - survived a little bit better. Here the houses are either built with public money and handed to a housing association (a private trust) or built by the HA. The HA then rents them out on similar terms to council houses. Because they aren't publicly owned the government couldn't sell them off. Except that because some HAs built using government loans or assistance the government was able to extend the right of tenants to buy to those homes too.
In the Netherlands we have the good tendency to take these away from politicians: any extra budget MUST be used to lower our national debt, not to lower taxes or 'buy votes' for the current people in charge.
This takes away the incentive to sell off public goods for their own short term profit.
The problem with this in the UK was that the stock of council housing became immensely valuable and as soon as we had a right wing government they started to sell it off. Selling it off created home owners (who are more likely to vote for that government) and raised "free" money which could be given out in tax cuts, so it was a natural target.
In the UK an alternate system - housing associations (HA) - survived a little bit better. Here the houses are either built with public money and handed to a housing association (a private trust) or built by the HA. The HA then rents them out on similar terms to council houses. Because they aren't publicly owned the government couldn't sell them off. Except that because some HAs built using government loans or assistance the government was able to extend the right of tenants to buy to those homes too.