Actually, no. If you have 10 houses and 9 are vacant and remain vacant then your nine vacant houses are contributing to the surplus that keeps rents high. Landlords not only rent homes but crucially, keep homes/units empty to control rent prices. Developers and landlords often work hand in glove with local governments to craft policies for just this purpose. Blackstone holds a high number of empty houses in their portfolio, it would be silly to believe that those homes are not capital.
Personal vs. Private property is not really an individual choice but a systemic set of incentives and consequences. What happens when one of the houses has property taxes that come due? What happens when the roof leaks and needs replaced? In the winter, pipes in vacant buildings are kept from freezing by running water, and there's going to be electric and/or water costs associated with that maintenance. will it just remain vacant while the owner hemorrhages money indefinately? If all ten units are empty and creating no income, and the owner has no plan to appreciate them as assets to resell them (because if the owner does, then they become capital) then is the owner really just like a wage worker, or do they have capital that makes them enough money that they can have 10 houses for personal use?
I'm sorry, but you are misunderstanding how capitaliam functions as a system. If someone has one extra house, maybe because of circumstances, I could see your point. But ten? No at that point they're practically no different from a landlord, as they are propping up rent prices whether they intend to or not. As long as there are ten families who need homes who can't get housing, that is private capital whether the owner uses it to make money or not.