The idea has some merit, but the greatest single disadvantage of his design is that no expansion of airport buildings or airport size is possible (they could go up, I guess, but there are limitations there, too); and the need to install subways for vehicular access to the airport infrastructure is also a costly and limiting factor.
You would need subways large enough to take the biggest construction equipment in and out, as repair and maintenance, and any building expansion would need items such as large cranes, earthmovers, etc., to be able to access the airport infrastructure.
In essence, the banked runway is a block to movement. You could build roads over the embankment, but then you have the additional hassle of juggling substantial numbers of vehicle movements across a very active runway.
I do not see the advantages of his radical design outweighing the disadvantages.