This was actually decided already. PETA sued on behalf of the monkey, and lost. The courts ruled that only humans can own copyrights. However, the issue of whether the photograph is copyrighted by the photographer or in the public domain was not decided. Personally I think that the photographer could likely win the copyright based on the effort he put into the setup, if he got a good enough lawyer.
To answer your thought experiment: Should an Art Teacher get copyright rights on all their students' work? (what you propose is effectively art college)
Agiain, to my mind the problem comes when someone (let's call him The Baron) employs a hundred Devs to make an AI that provides cheap legal advice, based on public-domain court records. People get cheap legal advice (society wins). The Devs get paid for their professional labour. A million lawyers go out of business. The Baron becomes astonishingly rich.
Should The Baron get all that value? Should the Devs? Should the out-of-work lawyers?
In quite a lot of cases they do (or at minimum the right to reproduce and distribute such at will without compensating the originator of the work).
https://www.trademarkandcopyrightlawblog.com/2012/05/bear-an...
https://designobserver.com/feature/who-owns-student-work/126...
https://www.huffpost.com/entry/who-owns-student-artwork_b_64...
My mother got hit with this when she tried to patent the seamless sweater invention she had - suddenly the university stepped in and said it was their invention. Sure enough, she'd signed over all copyright when she started the course.
but just because it happens now doesn't mean it's morally correct. In an ideal world, do we want this?
"Do I try to make my career defining art now or do I use this time to explore a variety of subjects and mediums?"
The fact the artist doesn't own the copyright to this early work tilts the question to the latter statement.
Can the same be said for AI/ML as they exist today? I'm not sure.
The fact remains, AI needs to be developed and trained by someone, and that completely affects the resultant "artwork". That's why people use the "photographer and camera" analogy. Does the Dev not deserve credit for their work?
(A thought experiment that I just came up with, not sure if it makes sense: Say you and I are locked in a room for a prolonged period of time. I tell you a bunch of stuff and you make some art based on it. Following the photographer/camera analogy, can it be said that you are my "tool"? Can I claim rights to what you come up with?)