Why should they? Copyright is an artificial restriction in the first place, that exists “To promote the Progress of Science and useful Arts” (in the US, but that’s where most companies are based). Why should we allow further legal restrictions that might strangle the progress of science and the useful arts?
What many people here want is for AI to help as many people as possible instead of just making some rich fucks richer. If we try to jam copyright into this, the rich fucks will just use it to build a moat and keep out the competition. What you should be advocating for instead is something like a mandatory GPL-style license, where anybody who uses the model or contributed training data to it has the right to a copy of it that they can run themselves. That would ensure that generative AI is democratizing. It also works for many different issues, such as biased models keeping minorities in jail longer.