I for one don't enjoy soviet apartment blocks.
I have to admit that I really prefer soviet apartment blocks to, for example:
* massive cramming of housemates in London, New York, San Francisco, or similar areas with rent going to a landed gentry
* to being saddled with mortgage debt which takes half of my post-tax income, with that going to a financial system
* to living outside of economically-viable areas, where cheap housing might be found, but where I have a lousy job
or many of the other pathologies of the current market. The capitalist model works just fine when land is cheap or free, as it was for most of America's history. Once it's about inherited land ownership and collecting rents, it breaks down.
However, in a democracy with public housing, you'd likely end up with something much nicer than soviet-style apartment blocks. Compare British health care to soviet health care.
Free markets tend towards a land-owning aristocracy and peasant renters being charged what the market will bear.
I'm not suggesting any particular course of action. I know of no way to move real estate into the public sector without the short-term transient driving the economy into the stone age. But if one were starting form scratch, that's definitely the way to go. It's more economically efficient and more equitable.
It's actually less about the houses on the land as about the land itself, but it's hard to decouple the two. Rent-collecting resources work best as a public good.
Private sector+heavy regulation isn't a mid-point between private and public. In many cases, including real estate and medicine, it's less efficient than either extreme.