I'll leave it to the linguists to debate UG and the specifics of what it does and doesn't mean, but commonalities like some sort of hierarchy, recursion, structure-dependence of rules, etc clearly exist, whatever you want to call them. By shared I just mean there's specific things that human cognitive faculties are set up to do and then other (often computationally simpler) things they clearly don't do. But again, if you're just saying natural languages are not formal languages, I guess that's true by definition. It just sounded to me like you were implying something different.