The lack of empathy is incredibly depressing...
It would be very easy to make training ML models on publicly available data illegal. I think that would be a very bad thing because it would legally enshrine a difference between human learning and machine learning in a broader sense, and I think machine learning has huge potential to improve everyone's lives.
Artists are in a similar position to grooms and farriers demanding the combustion engine be banned from the roads for spooking horses. They have a good point, but could easily screw everyone else over and halt technological progress for decades. I want to help them, but want to unblock ML progress more.
This isn't the only option though? You could restrict it to data where permission has been acquired, and many people would probably grant permission for free or for a small fee. Lots of stuff already exists in the public domain.
What ML people seem to want is the ability to just scoop up a billion images off the net with a spider and then feed it into their network, utilizing the unpaid labor of thousands-to-millions for free and turning it into profit. That is transparently unfair, I think. If you're going to enrich yourself, you should also enrich the people who made your success possible.