If they are indeed the output of "research" that couldn't exist without the requisite publicly available material, then they should be accessible by the public (and arguably, the products of said outputs should also be inherently public domain too).
If they are instead created products to be sold themselves, then what is utilized to create them should be licensed for that purpose.
Additionally, if they can be used to generate IP violating material, then IMHO, makes perfect sense for the rights holders of those IPs to sue their asses like they would anyone else who did that and sold the results.
Again, for emphasis: I'm not endorsing any of the effects of IP law. I am simply saying that we should all, from the poorest user to the richest corporation, be playing by the same rules, and it feels like AI companies entire existence is hinging on their ability to have their IP cake and eat it too: they want to be able to restrict and monetize access to their generative models that they've created, while also having free reign to generate clearly, bluntly plagiarizing material, by way of utilizing vast amounts of in-good-faith freely given material. It's gross, and it sucks.