> They end up having the opposite effect by making property owners less willing to rent out to anyone.
Yes, good! Then they will sell their bloody housing stock and people can BUY them instead
"Sorry bud, I know you just wanted a place to live while you went to college in this city but if you're not ready to buy a house we don't want you here"
That assumes that everyone who wants housing can afford to buy it rather than rent it. It also assumes that everyone who wants housing even wants to buy it.