Code without a copyright can generally be distributed and put in the pubic domain, and I wouldn't bet that the few existing court decisions won't be reversed.
But, the license reflects the rights that a copyright owner granted you; I don't see why laundering copyrighted material with training a model should remove the limitations on the material's usage that the author established.
So, while it makes sense to not be able to attach whatever copyright you want to LLM output, if it's the result of training on copyrighted code, the extent to which you're allowed to use it should be the intersection of the rights granted to you by that code's copyright owners.
It should thus carry a license that reflects the intersection of those rights.
What makes it much worse is that the model trainers don't tell you what specific sources determined the output, so you should probably just assume that it's the result of its whole training, and the only rights you have are those granted you by all the authors of the training material; and, this in all likelihood means no rights, for most LLM models in use now.
But, the license reflects the rights that a copyright owner granted you; I don't see why laundering copyrighted material with training a model should remove the limitations on the material's usage that the author established.
So, while it makes sense to not be able to attach whatever copyright you want to LLM output, if it's the result of training on copyrighted code, the extent to which you're allowed to use it should be the intersection of the rights granted to you by that code's copyright owners.
It should thus carry a license that reflects the intersection of those rights.
What makes it much worse is that the model trainers don't tell you what specific sources determined the output, so you should probably just assume that it's the result of its whole training, and the only rights you have are those granted you by all the authors of the training material; and, this in all likelihood means no rights, for most LLM models in use now.