The authors also zero in on a key example used to explain the “abundance” argument: comparing San Francisco and Houston. They argue that the price differences are not due to housing constraints, but likely due to changes in local incomes

That’s not what we see. There’s no difference in the effects of housing constraints on supply. For prices, there’s a gap, which the authors discuss in detail, but there’s no difference in *elasticity* (slopes are the same).

Others have argued that regulation reduces housing supply and drives up prices, hence why people are so focused on it.

New NBER Working paper on the big housing question (and one at the core of the "Abundance" agenda): Are regulations making housing scarce and unaffordable?

Nope.
www.nber.org/papers/w33576