LLMs really do find the signal in this noise because even just pre-training alone reveals incredible language capabilities but that's about it. They don't have any of the other skills you would expect and they most certainly aren't "safe". You can't even really talk to a pre-trained model because they haven't been refined into the chat-like interface that we're so used to.
The hard part after that for AI labs was getting together high quality data that transforms them from raw language machines into conversational agents. That's post-training and it's where the armies of humans have worked tirelessly to generate the refinement for the model. That's still valuable signal, sure, but it's not the signal that's found in the pre-training noise. The model doesn't learn much, if any, of its knowledge during post-training. It just learns how to wield it.
To be fair, some of the pre-training data is more curated. Like collections of math or code.