When someone rents a small apartment in the center of Paris for 4k on the private market in all likeliness they're paying more than 3k of pure rent profit to the owner.
The rent can be levied by the owner however the owner actually did not provide any of the investment or labor required to give the apartment the value it has. The apartment has value not because of anything inside the apartment or the building. It has value due to its location, something that the owner has no control over and did not spend a single penny to make more attractive.
This is obviously a huge inefficiency in the economy. Why should someone profit from the attractiveness of a location they haven't actually built? This is a positive externality.
Part of the solution of our huge housing crisis across most developed cities is obviously that there should just be more housing. This would bring prices down overall. However, new construction is extremely difficult, and that is due the in part to lobbies of wealthy owners which seek to keep prices high by maintaining scarcity.
Turning private rent housing into public housing is a good way to eliminate the economic inefficiency of rent in that one case and it also drives the price of nearby housing down too, as the private market has to compete with the public offering.