It was always a bit weird how heavily software companies leaned on copyright, and I think you could basically replicate the same intuitions and dynamics on top of trade secret law if you had to. KFC didn't go out of business when a Chicago Tribune reporter found what's most likely the secret recipe.

I'm also not sure that the current precedent on the matter is _quite_ as strong as you're thinking. The high-profile case you're most likely thinking of was from a guy Stephen Thaler, who was seeking not just to claim copyright on AI-generated content but to specify the AI as the sole author. (IIUC, he planned to still own the copyright on the theory that it was a work-for-hire.)