"Innate grammar" are essentially the meta-rules that govern why the rules are what they are. For instance, an English phrase can be recognized as valid or invalid by other native speakers according to the rules of the language. But why are the rules what they are?
This is especially puzzling due to the dazzling variety of human languages. And the fact that, after a period of immersion, humans seem to have the natural capacity to learn all of them.
How do LLMs fit into this? Well, I think it would be interesting if we left a group of LLM to talk to each other for 1000 years. Then see if 1) they developed a new language branch 2) that could be relearned by humans through immersion alone.
It's true that LLMs have learned (have they? I suppose that's a loaded word) human languages like English. But it's unclear if they are governed by the same meta-rules that both constrains and drives the evolution of humanities thousands of distinct languages.