I think there's a difference between completely impossible, and partially very difficult. If reasonably well-off people can pretty easily leverage low-interest rates and take control over property that otherwise wouldn't have as much competition, then that's probably a bad thing. The super rich will always figure out a way if it's lucrative enough, but those actions would stand out more if it was generally unacceptable. As it stands, I don't even know how to track down data on how many people own multiple properties. Likewise, you can't possibly out-pace multiple property ownership with supply in a desirable place unless you exhaust the excess capital available to wealthy people and ban low-density zoning codes and maybe even ban surface-level parking lots.

In my neighbourhood, lots of wealthy homeowners have signs up decrying the construction of a sky-scraper that's sort of vaguely near the edge of their neighbourhood, which is currently occupied by a parking lot. The effect it would theoretically have, is adding to the available housing supply in the area for people currently renting at absurd rates because it's impossible to buy anything. It would take away rental income from people who already leveraged themselves too much, and marginally decrease demand for their scarce commodity known as a place to live.