In practice, many of the cities with the highest housing costs are now strongly anti-infrastructure and anti-transport anytime it involves cars. (What good is a self-driving car if it's getting stuck in the same-or-larger traffic jam everyday?). Cities like this problem because it adds to the inflation of their own property values, and they get to pretend they are being "greener" or "safer" (even though self-driving EV cars eliminate the majority of those issues).
So I suspect that in practice, self-driving cars won't lower housing costs much in most major markets. It could help smaller cities, but they already struggle less with housing costs in the first place.
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The biggest changes will probably be felt elsewhere. Such as by professional drivers (school/city bus drivers, truck drivers, taxi/uber, etc). I also suspect some spill over against flights. It might soon be cheaper for a family of four to rent a self-driving Chevy Bolt to drive from ORD to MSP or ORD to ATL, than to fly there. Especially since, once you land in MSP/ATL, you'll need a car to get around anyway.
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Wealthy people will continue to be mostly unaffected, as they can already afford to live where they work, and can already choose to have no meaningful commute, anytime they desire to.