Code completion models can be useful because they output the most probable chain of tokens given a specific input, same as any LLM. There is no "signal" there besides probability. Besides, even those models are fine-tuned to follow best practices, specific language idioms, etc.
When we talk about "signal" in the context of general knowledge we refer to information that is meaningful and accurate for a specific context and input. So that if the user asks proof of the Earth being flat, the model doesn't give them false information from a random blog. Of course, LLMs still fall short at this, but post-training is crucial to boost the signal away from the noise. There's nothing inherent in the way LLMs work to make them do this. It is entirely based on the quality of the training data.
Base models (after pre-training) have zero practical value. They're absolutely useless when it comes to separating signal from noise, using any practical definition of those terms. As you said yourself, their output can be nonsensical, based solely on token probability in the original raw data.
The actual value of LLMs comes after the post-training phase, where the signal is injected into the model from relatively smaller amounts of high quality data. This is the data processed by armies of humans, without which LLMs would be completely worthless.
So whatever capability you think LLMs have to separate signal from noise is exclusively the product of humans. When that job becomes harder, the quality of LLMs will go down. Unless we figure out a way to automate data cleaning/labeling, which seems like an unsolvable problem, or for models to filter it during inference, which is what you're wrongly implying they already do. LLMs could assist humans with cleaning/labeling tasks, but that in itself has many challenges, and is not a solution to the model collapse problem.