It's probably not even possible to expand housing capacity to a significant degree in most locations it'd matters,
Even if it were, I contend the overall cost of living would go up dramatically (even in the hypothetical new high rises) due to transportation saturation and supply chain drama,
Also unless you literally double capacity everywhere what incentive do landlords (even new ones) have to moderate aggregate and individual rent growth? Since the state of the area is f'd today and demand is high, if there are any improvements demand can only go (dramatically) up.