The primary issue is the people that live in "no poors allowed" area can literally push the poors out of a voting area and thus use their "no poors allowed" policies to take over local governments. Which ultimately allows them to expand the "no poors allowed" zones.
Another major issue is there's a false impression about what's profitable when it comes to property ownership. That, in turn, drives up the price of property in a way no amount of "tent cities" can really compete with. In particular, landlords are using their freedoms to price fix and gouge. They've all realized that it's better to have 50% occupancy with 10x what a competitive market could bear (netting them 5x the profit of competition) then it is to shoot for 70% or 100% occupancy at a competitive market rate. And the cost of joining their ranks is high enough that there's really no option for a spoiler to come in and disrupt the market.
Further, we have the freedom of airbnb which has recognized that if you pay a rate that's 30x the cost of rent you only need rent a property out once a month to turn a profit. And, as it turns out, that rate is often somewhat competitive with a hotel.
All these freedoms give property owners massive extractive power against the working class.
Zoning, IMO, is a red herring to the real problem. You can fix it, you can not fix it. It really doesn't matter because builders very often are participating in exactly the same structure and they aren't going to build themselves out of profit. Looser restrictions will mostly just mean they'll spend even less delivering homes while still charging the same rates because their rates are based not on a market but rather on the income of their tenets.
The fix is a brutal one. The poors need to understand the predicament and vote for politicians that will serve their interests and not the interests of the property owners. A very hard uphill battle because property owners have a lot of money and politicians can be unfortunately easy to buy.