I think we're already getting a taste of it with copyrighted but publicly accessible works getting fed into the training step of AI models. The economic benefits of this training then accrue to the model's owners, while the creators of the training data have to pay for access.
It seems as though AI models improve with more training data, so I expect AI companies to come for ostensibly private data next. Microsoft is actually really well positioned here since they've already acclimatized their user base to transmitting an endless stream of telemetry and they own the dominant desktop/laptop OS.