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.
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.
Demand is out pacing supply because while the greatest and silent generation was happy to retire on stonks, pensions and bonds the boomers all went out and bought more and more homes and condos and whatnot for rental income.
It used to be that rental housing was either owner occupied, like a landlord living on one side of a duplex or it was a big commercial investment. The current trend of every idiot having their starter house from 20yr ago listed as an airBnB wasn't a thing back then.
So basically we "need" way more housing per capita now so that they can all have their stupid little side gigs.
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.
If people had the wealth to own land and build on it then they'd build their own.
It can be both. Wealthy people make it illegal to subdivide large housing units.