If bread were in short supply and lots of people needed it, prices would rise. We could count the number of people and slice loaves equally, stagnate the production, and as more people needed bread, slice thinner and thinner. Everyone would be equally hungry, whether they could pay for a bigger slice or not.
Or, the baker could bake more bread so that anyone who wanted it could get some. People with less money might get a thinner slice or fewer slices than others, but the price would go down; the baker would make more money, hire assistants, and open more bakeries, increasing the supply; and there’d be more jobs, more tax revenue and competition would keep prices low. In other words, everyone would get more bread.
So it is with housing: either distribute less and less to greater numbers of people (which in our current situation, has led to people crowding together into the same units, amounting to the housing version of a “thin slice”). Or build more. The choice is equity and rationing or opportunity and lower prices.