>Some amount of knowledge is required for reasoning.

This is the root of problem. If you think about STEM universities, they don't really teach you things you need in the real world. They teach you what you need to know in order to go out there and accumulate the necessary information which can then be used to solve problems. Giving a person access to the internet or a super powerful calculator (like Mathematica) won't mean that they can do anything useful. They need tons of experience to use these tools in an effective way. That experience is basically all that implicit adjacent knowledge that we pick up along the way getting our degrees. And LLMs pick that up during pre-training. Drop this part and the outcome will be worthless.