It's not just foreign money. Private equity firms, wealthy speculators and cheap Fed money are a big part of it as well.
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.
Are they permitted to rent them out and not pay? If so it seems like it would be a great loophole for a bank to mutate into a quasi real estate management company. You could easily undercut any other local rents by the cost of property taxes.