That market is so segmented and fractured. Not to mentioned very few of the Wall Street companies by much of anything outside of the "Sun Belt" and if they do the volume is absolutely miniscule.
Most of these companies are public, you can see the data for yourself in their latest earnings.
Of note, institutional investors sell assets every quarter as well.
I'm not advocating for these folks, I don't work in this industry. But I have in a previous life. They could grow, but right now they are not what is causing or has caused housing problems.
Look at Utah. Hardly any of the big institutional investors own much of any inventory in Utah but things are crazy here. It isn't the investors causing problems here.