Might not a solution to both problems be high property taxes for unoccupied housing? If you are buying purely to park your cash, and effectively take those units off the market, some strong disincentive should exist.
The housing isn't vacant because it's not occupied. It's vacant because the owners have their primary residence elsewhere. Or have several homes. London has neighborhoods where full time residency runs around 30% as well, leading to "ghost towns" - supposedly much of that is Russian or eastern euro money being kept outside of their home countries less as an investment than a value store. I have a friend who is about to close on a condo in LA - all cash - and already owns homes in Asia and New York. She views them as investments but having paid cash she has no interest in renting them out.
I wouldn't consider these investment properties occupied. And in fact, that's the point of my suggestion. Excess liquidity accumulated by the upper echelons of society is spurring this "housing crisis". Society has an interest in dis-incentivizing the kind of property-hoarding that you describe.
In addition to wanting to keep housing affordable for workers in cities and elsewhere, cities should be scared witless by the thought of "ghost towns" and neighborhoods with 30% residency. Cities are not collections of streets and buildings, they are made up of the people that reside in them, and without people, the economy of a city will collapse.
The disincentive is the money that renting out your units would bring in. If they're so worthless (to everyone else) that they wouldn't rent for a noticeable amount, who cares if they're taken off the market?
