From copyright.gov "Copyright does not protect facts, ideas, systems, or methods of operation, although it may protect the way these things are expressed"

What rights does copyright provide?

Reproduce the work in copies or phonorecords.

Prepare derivative works based upon the work.

Distribute copies or phonorecords of the work to the public by sale or other transfer of ownership or by rental, lease, or lending.

Perform the work publicly if it is a literary, musical, dramatic, or choreographic work; a pantomime; or a motion picture or other audiovisual work.

Display the work publicly if it is a literary, musical, dramatic, or choreographic work; a pantomime; or a pictorial, graphic, or sculptural work. This right also applies to the individual images of a motion picture or other audiovisual work.

Perform the work publicly by means of a digital audio transmission if the work is a sound recording.

Training an AI isn't on this list. An AI may produce infringing outputs, but training an AI isn't a violation of copyright.

"Copyright laundering" is a nonsense idea. Copyright is not designed to prevent people or machines from producing things in a style or similar things. It protects against exact reproduction or reuse, and that only to the extent that the form is separable from function. If the form is inseparable from function, the expression cannot be copyrighted at all.

Let's assume "shuffling stuff" as you describe it would solidly place a work into the "derivative works" category.

Fine, the AI has produced a derivative work. The original copyright holder has a claim on that work if it were to be distributed, sold, displayed, or performed.

Does the AI hold a copyright? No. Only humans can hold copyrights. Does the prompter hold a copyright? No. A human has to perform the transformative work, not merely arrange for a machine to do it. AI outputs are not copyrightable.

But how you "feel" about it isn't a useful measure. It being like "cheating off someone's homework" isn't useful, either. Hell. Copyright is carefully crafted to allow "cheating off someone's homework" provided that the result doesn't reproduce elements of the original exactly.