What makes you believe this? If rentals were illegal, then there would be an entire cottage industry spring up around creative ways to lend people money who can't necessarily afford it. Which seems like a way to drive up purchase prices.

Plus, in the most unaffordable places in the world, rental prices are dirt cheap compared to purchase prices. In a lot of these places, rental income is so inconsequential, that places sit empty because owners don't want to deal with renters, since most of their return comes from appreciation. Which suggests that rental prices are completely detached from purchase prices.