Australia has ownership rules in place that generally restrict foreign purchases to new build developments.  The theory was, that overseas money would provide an impetus to build projects (and provide financing) that may not otherwise get built, and those units would end up in a domestic rental market.

Surprise, surprise.  Overseas money flooded in, but purchased  100% of the development, and many of the housing units were simply left empty. Or continually flipped and resold offshore.

Australia is now restricting offshore presales to 50% of a development, and imposing taxation if left sold and vacant.

You make a great suggestion about purpose built rental housing.