You could still have different prices, albeit lower ones. Renting then becomes part of a resources allocation game. If you want a bigger/more luxurious home, you pay more and have less for other things. If a fancy house isn’t so important to you, you can get a cheaper one and have more money left for vacations, fine dining, cinema, etc.

As for the efficiency, that government department could take lessons from big property owners and organize like them, only with state subsidies and without profit goals. That way, the middle class, by virtue of having more money, could still afford better housing. Also, I don’t want the middle class to live like the working class, I want the working class to live like the middle class. Also also, there’s no “middle class”, only parts of the working class that got lucky. But they’re fundamentally still beholden to their employers’ whims.

Incremental change withing the current system is good and important, but we nonetheless have to discuss the big break that has to occur at some point, and what comes after. Incremental change can only take us so far.