Comment by Workaccount2

>will buy the extra supply and rent to the poor.

The wealthy are generally monetarily shrewd, and building homes makes home ownership a worse investment. If there is a deluge of homes being built, the wealthy will take their money elsewhere. Being a landlord typically has ~10% annual return. Compared to just sticking money in the stock market, it's actually been worse as of late.

The goal of the wealthy isn't to make people suffer, it's to maximize their ROI.