that's was doable back in the USSR and doable today in China. In US it may be easier to build right in the ocean :) For building huge structures 10-20m depth is almost like land and you get added benefit of being able to plan and build all the infrastructure from scratch instead of trying to upgrade and be constricted by the limits of the old. You can build another San Francisco sized city near by just at the cost of the steel and concrete it takes. Smaller number of square miles with 100+ stories high interconnected structure(s) - of any shape/form one can come up with as without historic parcelization you wouldn't be limited to the narrow tall buildings of the standard cities.
>10 story apartments and there would be no crisis whatsoever.
how about infrastructure? water/sewer/electricity/roads?
Well, you'd get a different sort of crisis, where plunging rents would make landlords unable to cover the cost of the new construction. I agree that we need more housing, though.