Because multi-family buildings (required for higher density) come with more complicated ownership models. Owner occupied triple deckers in Boston, for example, often come with their own condo associations because there needs to be some way to handle the shared maintenance and expenses.

That's for a three unit building. Now scale that to a twenty or one hundred unit building. At some point, it makes sense for a single entity to handle the common maintenance through outright ownership and rent. Individual families have the flexibility to leave if things suck without being financially tied to the building long-term and subject to changes in housing prices. Yes, moving as a renter is expensive. It's still lower cost and friction than moving as an owner.

Source: rented for years in cities. Now happily a homeowner in the hinterlands of Vermont.

One thing soviet commies did right was housing builds. Build factory for city blocks, then just pop them up, constantly, keeping the line busy.

It should really be city that is building the new housing (even if in the end it gets subcontracted, at least the top level have vested interest in keeping the quality and cost in check). Maybe even offer some rent-to-own programs where part of rent gets put into savings that can be used to either buy it after few years of use or be withdrawn when moving so renter have nice lil bit of money to put forward for buying new apartment/home.

Then the city can actually plan for it, rather than hope housing developer that bought the land does something good for city and not just their own pocket.