OP never talked about art. Design is not art, it's problem solving. And good design according to Dieter Rams:

1. Good design is innovative 2. Good design makes a product useful 3. Good design is aesthetic 4. Good design makes a product understandable 5. Good design is unobtrusive 6. Good design is honest 7. Good design is long-lasting 8. Good design is thorough down to the last detail 9. Good design is environmentally friendly 10. Good design is as little design as possible

Generative AI just tries to predict based on its training data.

>"design" explicitly relates to products not art

a product can be a piece of art and design can and does in practice often go hand in had with art, practically most designers also other than the utilitarian role practice the artistic one, wether you would want to group art within design as one is a matter of definitions