Could just be that this is often done using GANs? So if you come up with some better way of telling apart real from fake, it can immediately be used as part of the discriminator, resulting in (hopefully) even better fake images.

> So if you come up with some better way of telling apart real from fake, it can immediately be used as part of the discriminator

The generator can only learn from the discriminator if the discriminator is differentiable and has reasonably consistent gradients.

You can use relaxation for discrete variables (e.g. by using convex simplex), replacing them with differentiable variables, and then just discretize after the very end of the computation. A common trick for variational autoencoders that are another way to do generative models.

I sort of naively assumed that any binary classification task on images nowadays would be done with a deep NN.

Are there any proposed techniques for detecting fakes that can't be easily differentiated through?

To my understanding, the idea is to stop training as soon as the discriminator has been 'fooled', i.e. its performance for telling fake and real images apart is just like random guessing. So, in a sense, you always keep on making better fake images, but not necessarily better discriminators (unless you botch the training or the losses, obviously).

Another reason (next to the ones about GANs etc. that have already been mentioned) is also that it's easier to fool detection systems by just making up more data---there's a heavy imbalance going on here, and that does not even account for issues with real images, such as artefacts, or damage, and so on.

There's more money in fakery than truthery.

GANs are detectors too, so at any point in time they will be right-on-par with the state of the art fakes, but no better.

One thing that comes to mind is the significant cost asymmetry of a false result or error.