Alternative idea if you want a more capitalist solution than government owned and distributed housing would be mandated rent to own. End of year, current owner tallies up all expenses, anything over is used to purchase equity at market rate. You either sell the equity when you move, or eventually own the place. No landlords just a delayed title transfer.

Of course this wouldn't solve the fact that housing is a human right that all should have access to but any capitalist solution requires a "loser" to suffer some form of horror