I think discussing the copyright status requires making some distinctions, because this is multiple versions of multiple technologies.
It is possible that the royalty-free terms of service of some of these AI art services will be upheld, though given how copyright friendly and public domain apathetic the US courts where the matter will most likely be settled are, I'd bet on those images ending up copyright protected.
Meanwhile, I think the people who actually are serious about making art with this technology for a finished product are going to end up running Stable Diffusion (the license to which makes to claims about the outputs) or the comparable things that will supplant it, on local PCs where they can fine-tune the operations of the program, then manipulate iterations and reprocess them. A single final output of the program will almost never be as good as what could be created by manually compositing together several of the slight iterations of the final output, so there will likely be some substantial transformative use at the end compositing images together, even if somehow the underlying AI art was, improbably, ruled non-copyrightable.
And, of course, I think a lot of art will be created by manually heavily modifying the outputs of all these programs, or incorporating outputs into larger compositions.
In other words, AI art is not and will never be a single monolithic thing, it is several technologies, with different license agreements attached, being used in collaboration with various levels of human manipulation. I think it can safely be assumed that people own a copyright in the things that they created with AI on their own computer, under a permissive license, and substantially altered manually, provided it doesn't infringe excessively on someone else's copyright image. Everything else is up in the air, and going to require some court precedent or new laws to iron out.
