Great article. And you're absolutely right; this is a huge deal that needs to be figured out quickly. I don't think typical copyright is a good approach, mind you. To me it's obvious that the explicit use of a living artist's name in a prompt is a direct use of that artist's intellectual property. No doubt whatsoever. Some sort of license or royalty seems like a reasonable middle-ground.
It's difficult to properly appreciate when we see so many images cribbed from Picasso or Van Gogh, since these are long-dead artists whose work has become a kind of decorative feature of public space as a whole. But imagine when these technologies extend to music or film. If you have an app that can generate a continuous stream of new Beyoncé songs, do you really think Beyoncé is entitled to nothing? Do you think that the startup that released the app, or the VC firm that backed them, owe nothing? Taking a complete style only appears to be different because it depends on the exploitation of a high-dimensional parameter space—you are stealing from the source artist on a bunch of subtle formal levels, too complex to easily quantify. But your work is still utterly dependent on that artist, and for that reason you should share any financial benefit.
Ultimately, business (and probably government) needs to start figuring out how to align financial value to human value. Our current approach is far too simplistic and completely insufficient for the technological landscape that is at our doorstep.