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.