Citation needed, my understanding was that housing prices are being driven up by real estate owners/agencies buying tons of property to either rent at extortionary prices or sit on until they sell for a higher price to the next sucker. Also stuff like the RealPage scandal where they simply illegally collude: https://news.ycombinator.com/item?id=41330007
I think the idea of a law that only allows a limited number of owned properties per person and requires them to actually be using those properties would be interesting to alleviate this.
Housing prices are being driven up by the fact that we don't build enough housing. That should be the end of the discussion. What you describe is just a symptom of not having enough housing. If we just built more housing then there wouldn't be any business angle for the corporations buying up housing.
The obscenely rich entities that buy up tons of property without actually using it do so because they only stand to gain even more money on it later. Making more housing would help in the long term for sure, but these entities would still buy up most of it as it becomes available. Remember that as long as they hold the vast majority, they essentially have a captive audience and can set whatever outlandish prices they want (especially when they collude as they have done). Something to restrict the number of unused properties a person can own would still be beneficial either way.
This also goes without mentioning the restrictions on "just" building new housing (land, time, and space, particularly space located near job sites).
I think the idea of a law that only allows a limited number of owned properties per person and requires them to actually be using those properties would be interesting to alleviate this.