I'm not sure I agree that LLMs solve for the statistical mean

But more importantly: isn't what you call "intent" just a series of optimization goals? You want your code to satisfy the constraint of being correct™, while also maximizing various other goals like being maintainable, easy to understand, having few lines of code, as little tight coupling as possible, etc. Goals that often conflict, but when given two implementations you could likely tell which hits the better tradeoff (in your engineering experience)

Those are all things that theoretically - with a tight enough specification and enough compute - a constraint solver could solve. No human intent necessary.

The issue is more that we can't fully specify all those side goals, and even if we could the LLM would struggle following them. A classic paperclip maximizer problem (where nobody told the paperclip maximizer to keep the planet inhabitable and all the other side conditions we implicitly assume)