For a long time I wondered where popular misconceptions about facts(usually historical) came from. Then I read about the history of the Encyclopedia Britannica and its checkered editorial history and realized I had found the cause: we relied a lot on truth-making authorities in the past, and they wrote in their biases.
So when we speak of intentional creation, we are in some ways looking a mode of truth reminiscent of Britannica: the world as someone experienced and described it, biases and all. Neither a sensory truth like "it feels cold today", nor an emergent collective belief like our rules of language.
What makes the LLM chatbot interesting is that it resembles a lens into collective belief; it starts with one bias, but you can tell it, "now explain it the way this other type of person would," and it will oblige you with its best in-character approximation, changing facts and details as well as aesthetics. It is capable of deep and radical changes to its output with minimal changes in prompting.
That's something that you could access in a limited sense with traditional PCG, but almost entirely in terms of mathematics operating on premade assets - fractals and chaos functions and so forth. Here you have a "fractal encyclopedia", working over an enormous reference library. It can, in fact, attempt to place every brush stroke "in the style of a Dutch master" if recursively prompted to do so, although in any existing implementation, you will run into technical limits with its dataset and working context. But if we look over towards diffusion model image generation, we know that that general idea does work - it's always a little less exact than the original human, but it can get us far past the uncanny valley.
And that's valuable because all the human creative stuff is built on references, too: original ideas emerge in one context, then get transferred to another. So there's a sense of, yes, you can definitely build a "make game" button here, and it'll be an approximation of a hypothetical human character that built the thing, but you can easily turn that output into a reference for something else that injects more bias and humanity into it or adds more structural rules to rigorously shape it. Often that's the actual path of creativity: make a longer pipeline of refinement with more layers to it, and you end up with an increased sense of transformative elements and intentional structure.