The laws are currently the same for everyone when it comes to what you can use to train an AI with. I, as an individual, can use whatever public facing data I wish to build or fine tune AI models, same as Microsoft.
If we make copyright laws even stronger, the only one getting locked out of the game are the little guys. Microsoft, google and company can afford to pay ridiculous prices for datasets. What they don't own mainly comes from aggregators like Reddit, Getty, Instagram and Stack.
Boosting copyright laws essentially kill all legal forms of open source AI. It would force the open source scene to go underground as a pirate network and lead to the scenario you mentioned.