"If there was actual demand for denser housing or office space you'd see it sprouting up across the river in Virginia or outside the southeast of the city where land is dirt cheap."

This is untrue. If housing desirablility is inversely proportional to the distance from the White House, then the area of equally desirable housing increases with square of the distance. You won't get dense nodes. It'll be spread around in a circle.

"this will not lead to affordable or convenient housing"

The more housing you allow, the cheaper it will be compared to a universe with supply restrictions. Do you disagree with that?