A world where you cannot rent is also one where there isn't a huge class of people who own more housing units than they could possibly live in.
I don't believe they exist.
If you are referring to corporate owners of apartment buildings, that's one thing. But to say there is a huge class of people who are landlords is just unrealistic. Very few people own more than one home, and even fewer people own more than two.
To wit:
> Of the approximately 50 million rental housing units in the United States, around 41% of the rental units are owned by mom and pop landlords, also known as individual investor landlords. That means approximately 20.5 million units are overseen by mom and pop landlords.
https://getflex.com/blog/landlord-statistics/
Also, from the same site, the average landlord has 3 properties. That means there are more than 6 million individual landlords in the US. I'm not going to nitpick whether that's "huge" or not; the point is proven.
In a population of 330 million. That's ~1.8% of the population. Hardly a "huge class".