Except you need cash flow or savings to afford a house, even a paid off one. If you don't pay your mortgage or tax bill, then someone is going to evict you.

I don't understand the criticism, because the cash-flow aspect certainly doesn't get better with options beyond a wholly owned house...

Houses aren't great protection against homelessness because they don't address the root cause of being homeless: having no money or income. They can provide a buffer because it's harder to foreclose on a person than it is to evict them. While this additional time may certainly make a difference, in all likelihood the outcome of losing a job and not being able to find another one is probably the same.

You can't liquidate any built up equity either, since you probably need income or assets to get a rental or equity loan. So it's completely possible that you lose any built up equity in the event of a foreclosure too.