Simpler "fixes": Prevent corporations from owning single family homes and don't allow anyone to own more than one single family home.

It'd crash the housing market, making homes MUCH more affordable, immediately. As corporations—who currently own 25% of all single family homes in some markets—are forced to sell off their inventory.

They could still own multi-family dwellings, just not single family homes.

The wealthy would just build multi-family dwellings for themselves, owned by corporations (that they own), and rent them to themselves. So it wouldn't really interfere with their rich lives much.