Do we? I've found Github Copilot fairly useful, several chatbots have built-in code interpreters to allow the LLM to answer queries by writing and evaluating code, and I've seen demos/startups using AI to generate websites and small basic games.
Certainly there's still a ways to go before reaching human level, but I wouldn't feel safe saying we know it's something LLMs "cannot do".
> you have no choice but to tell it EXACTLY what you want. Free form language requests are never going to get you there
I don't see any fundamental limitation in this regard compared to the level of detail you'd need to give a human programmer. With existing integrations you can already ask along the lines of "fit a model to this dataset [attachment]" and have it infer a lot of the details, then iterate on it with clarification as you could a human programmer if needed.
AGI will have to come from another direction