proof-of-work based blockchains are technically also an arms race between good and bad actors. It still works because extending the chain costs compute, so as long as the good actors have the majority of compute, all is well.
Training a GAN can be thought about as a proof-of-work type job, where you need to recover the best Generator from the SOTA Discriminator, or vice versa.
So the proof of work chain looks like D-G-D-G-D-G. As long as the good actors continue to dedicate more compute to tackling deepfakes than bad actors, I think it should help mitigate the issue.