That sounds like their problem, not ours.
And I think that is where we'll end up. It won't be as bad as you think; new types of agencies will negotiate with studios and publishing houses and compile and license data to the AI companies. A new infrastructure will gradually emerge. Unions, client agencies, publishing houses, regulatory bodies, licensing boards, all these organisations emerged to resolve various "difficult" problems over the centuries. But the difficult licensing problem isn't that difficult--it's not rocket science, and industries will adapt to accommodate it.
An AI company will license one or more data sets from an agency, which itself will have gathered and compiled that data set by licensing the content from other companies, some of which will deal with the owned IP of entire studios, others of which will deal with individual artists. It'll all be one massive filtering system, lots of people will get rich being the middle-men, but it's very doable.