I will get excited for/scared of LLMs when they can tackle this kind of problem. But I don't believe they can because of the fundamental nature of their design, which is both backward looking (thus not better than the human state of the art) and lacks human intuition and self awareness. Or perhaps rather I believe that the prompt that would be required to get an LLM to produce such a program is a problem of at least equivalent complexity to implementing the program without an LLM.