This is not the point of that Babbage quote, and no, LLMs have not solved it, because it cannot be solved, because "garbage in, garbage out" is a fundamental observation of the limits of logic itself, having more to with the laws of thermodynamics than it does with programming. The output of a logical process cannot be more accurate than the inputs to that process; you cannot conjure information out of the ether. The LLM isn't the logical process in this analogy, it's one of the inputs.