Why would they sit on them?

Surely they are more likely to sell if they can never be leased profitably? This would put that capital to better use.

Your assumption there is also that the class of ‘renters’ is homogenous and wants to rent. In some cities there is a significant class of people who are forced into continuing with renting because of supply constraints on homes for sale, which are exacerbated by landlords with superior access to leverage buying up stock and pushing up prices. In this situation the landlords actually create their own market.

A comparative shortage of rental properties and of landlords could be very desirable, as it implies more owner-occupiers.

It also implies more capital flowing out of real-estate and into productive industry, which one would assume is also desirable for a thriving economy.

What happens is that economics shift from a renewable model to an extractive model.

Farms are renewable so farmers maintain them over centuries. Mines are extractive so they get pumped and dumped.

What landlords do in these situations is try to extract as much money as possible before the enterprise collapses, either literally or figuratively. New housing doesn't come online quickly so both quality and quantity fall.