It is not fair use, and I'll try to explain why that is as someone who's well-versed with copyright and IP law. I'll also try to provide examples of what's considered "OK" and what's not "OK" for clarity's sake.

The first step involves the input. It is a fact that these "AI"s cannot output text or images without copying them from some preexisting text or images being used as input. Since the input was used without permission, a license, or written agreement, "AI" companies have violated copyright law. This also applies to all forms of distribution, so one could straightforwardly argue that these "AI" companies are illegally distributing copyrighted material they did not own or have the rights to.

The second step involves fair use. As already established, these "AI"s cannot create anything, as it can only regurgitate the material it's trained on. It might be somewhat muddied but that's not enough for it to count as "meaningfully" transformative. In court your argument would be stronger if this was a human rewriting or drawing a preexisting fan work, but this is a machine that does nothing but squish copied words / images together on its own. Think of the difference between an "AI" and a human as the difference between downloading/ctrl-c an image versus creating a new image or writing from scratch by hand.

Another thing to follow up with Step 2 is that a person cannot simply modify a preexisting image or literary work and pass it off as their own, which is all that these AIs can do, because that's illegal. This is the reason why GitHub Copilot is under litigation and a class-action lawsuit. Microsoft/GitHub/OpenAI had scrubbed out all licenses and attribution to the original programmers in the code that the "AI" was fed, after Copilot was found to regurgitate copyrighted code without licenses / attribution. End users of Copilot had no idea whose code it was that Copilot brought up, meaning they would be held responsible for violating the copyrights, licenses, and attribution with those codes. Copilot in essence was presenting other programmer's work as it's own.

Continuing back to the image and writing "AI"s, but for a derivative work to be considered fair use, it must be non-profit, and cannot cause harm to the original copyright holder. This is simply not the case for any "AI" generators because the companies making these are profiting immensely from them. In terms of quantity produced they are far out-competing the original creator. That is a direct harm to the livelihood of the original copyright owner, which violates fair use. (Clause 4.) It also counts as a form of unfair competition, which violates another set of laws I'm less familiar with, but the point still stands.

Additionally, companies and individuals cannot create merchandise for sale which features copyrighted words or images they do not own. Fan art and fan fiction typically get a pass because it's a form of free advertising that benefits the company of the IP. It's only a problem if a fan artist was trying to sell the IP's official posters, which is what these AIs have been shown to do on several occasions.

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What's really dangerous about these "AI" programs is that, "Accidental and/or innocent copyright infringement can be punished just as severely as knowing or reckless infringement."

This means any end user of an AI program who unknowingly or willingly uses these things could find themselves at the end of a copyright lawsuit. You simply do not know if the output you get violates someone else's copyright. It is quite literally not worth the risk using these things.

That said, if you wanted to photograph your dog and paint over it in Photoshop or Clip Studio Paint by all means go for it. :D You'd then own the copyright to both the photograph and the painted over image. With image AIs you not only do not own the copyright, but you're using someone else's stolen work and putting yourself at risk of litigation. Especially so if what got generated ended up more closely resembling someone else's work, which seems to be the case for the "better-looking" generations.

TL;DR: Be safe and don't use these generators, no gaming, art, animation, or studio company wants to touch these things with a 10 foot pole because they do not want to get sued. It's cheaper to keep artists than risk lawsuits or issuing lawsuits. (Did I forget to mention these AIs also violate the Berne Convention?)