Here's the behavior of PE firms when it comes to renting houses, they rent them out and charge for everything:
https://www.nytimes.com/2020/03/04/magazine/wall-street-land...
As for the vacancy rates, how do you know the homes are vacant, and what is the proper vacancy rate? These can be looked up in from Census ACS estimates, though I hear that the Post Office sometimes has better data.
I would say that a healthy vacancy rate is at least 7%, possibly higher.
If anything, Vancouver is solid evidence that vacant homes are not the problem, despite so many current homeowners being desperate to use them as an excuse not to build more homes. In Vancouver, the tax provides a small income stream, but has changed nothing at all structurally. And that's in combination with the foreign purchaser tax.
The one solution is to start building what people want, what you derisively call "stack and pack", in sufficient numbers over a long enough period of time to satisfy everyone's desire for housing.
We are not off the mark by 10% in the amount of homes needed in LA or the Bay Area, we are 30%-50% off or more. We have been under building for decades now.