The problem is that it's pretty easy to fine tune an adversarial model to fool classifiers. In some sense, building that classifier is a very productive way to improve the model, so it's something the generative side is already doing. That makes it hard to win the arms race from the classification side.
But also the solution. With enough classify -> beat the classifier iteration, the works will be indistinguishable from human production, at which point there is no longer a need for classification.