Structural Integrity Response

They couldn't be built on the corners because it would compromise the structural integrity of the building, which is a very bad thing.

Its major flaw is that the planned design of the structure’s supports wouldn't be able to hold the mass of the building when confronted with very strong winds, and the odds of such winds were too high, especially considering the potential collateral damage that could be done.

A young undergrad student discovered this flaw.