Chatbots don't have physical bodies that require food and shelter. So even if you could prove their creativity was identical to real human creativity and not a crude imitation more akin to assembling random collages, they still don't deserve the same protections as real artists with physical bodies that need food and shelter.
Which isn't even approaching the obvious retort that their creativity is a crude imitation of real creativity.
Copyright doesn't exist because there's some important moral value to the useful arts. It exists to keep food in bellies.
You're bending over backwards to protect bots as deserving identical rights to humans. For what purpose should they have those rights? The only benefit to treating the bots this way is to ensure the rich tech oligarchs that already have undue power and influence in our society get even richer and get even more influence.