We've been doing it for genetic modification for ages. If it's possible to stop people from making human-chihuahua baby hybrids en masse, why is it impossible to stop people from culturally devaluing art en masse?
I don't think it's reactionary to have a cultural concern like this, either. Especially when the concern boils down to hyper-commodification. I'm not concerned about some abstract "rot" of society, but rather the commodification of art itself.
Capitalism has already commodifed so many aspects of art production even without large neural nets. Think about the fact that the "industry-accepted" tools are all proprietary and behind exorbitant SaaSS/pay to rent models (both hardware and software). Neural nets didn't change much but just make copyright law even more a failure than it already is.