Deregulation simply allows capitalists to more easily exploit their leverage as landowners. It will not create more affordable housing anymore than eliminating food safety inspections will create more affordable food.
Developers don't want affordable housing. They won't continue developing beyond the demand, because that would devalue their existing investments.
If you want more affordable housing, you need specific regulation requiring it. We could also restrict commercial investment in residential property, or tax corporations out of the market entirely. Deregulation just feeds the beast that's eating you.