Where's the evidence that wealth inequality is the root cause of housing shortage, as opposed to say, the real and factual lack of building?
Even if the wealthy did buy up extra supply to rent out, that would only mean increased supply of rentals, which would lower rents.
Want something really interesting? There's a pretty decent chance that our wealth inequality is entirely caused by restricting housing supply. ;)
The ultra wealthy don't even care if it's rented, they're just diversifying their asset portfolios.
It can be both. Wealthy people make it illegal to subdivide large housing units.
If people had the wealth to own land and build on it then they'd build their own.
Not commenting on the ethical side of it, in many instances rentals are just a side income, the real value is in the increasing price of the house due to demand outpacing supply. See https://news.ycombinator.com/item?id=37855625 for past discussion on this.