I think the misconception is actually the opposite - focussing too much on the method rather than the output. Bread is not just yeasty-wheat - if you mix bread and wheat together and apply some heat you get something a little surprising. I think the same is true for LLM's - in the task of training a next-word guesser there are emergent capabilities which end up going beyond what people expect when looking at the method.
Yes, it is designed to statistically guess the next word, but in order to do that the LLM has (surprisingly) gained internal representations of things like 'what is a giraffe'. In order to do the task of 'what is the next word' most effectively, it has had to understand/learn about about the world.
Can you provide an example where you think GPT-4 performs badly that proves your point? (i.e. something not in the training corpus that I could probably answer but a leading LLM could not)