The tandem option is also viable, and is actually a really great starting place for this sort of thing (I will fully acknowledge that my proposal would be very difficult to get through any current political system). The public sector deliberately competing with the private to bring down prices has been proven to work. A great example of this is Sasktel in Canada, where the provincial government made their own publicly owned telecoms provider, and as a result all the big telcos, that functioned as an oligopoly everywhere else, offering identical plans at identical prices, had to offer plans that were much, much cheaper in Saskatchewan specifically.

Also there's absolutely room for debate as to whether a single massive rental company would be better, or whether it would be preferable to have lots of small, regional or municipal corps. I prefer the former only because it would give them more flexible buying power in terms of scooping up properties to rent out, but I'm sure there are strong arguments for the other approach.