At this point we're already using different definitions of grammar and vocabulary - are they discrete (as in a rule system, vide Harper) or continuous (as in a probability, vide LLMs). LLMs, like humans, can learn them on the fly, and, like humans, they'll have problems and disagreements judging whether something should be highlighted as an error or not.

Or, in other words: if you "just" want a utility that can learn speech on the fly, you don't need a rigid grammar checker, just a good enough approximator. If you want to check if a document contains errors, you need to define what an error is, and then if you want to define it in a strict manner, at that point you need a rule engine of some sort instead of something probabilistic.