Describing it as a "next-token predictor" in the sense that this would mean it's fundamentally limited to just a fraction of an inferential step is doubly wrong:
1. In order to select even the first word of a meaningful sentence, it already has to have structure and meaning of what follows captured somewhere inside, mostly in it's weights/activations or indexed by it's state vector.
2. What you see when you use an LLM is not next-token prediction directly next to the prompt, but instead following a block of varying length of next-token prediction that happened to make progress on the problem in your prompt, and which just summarizes the results.
Even so, one might wonder why we don't try making systems that take different approaches. For example, after a traditional first pass of output, they could do sliding-window "optimizations" considering each token in the context of tokens both before and after, and possibly replace words or phrases in-place.
For example, I've noticed quite a few cases recently of LLMs outputting "but" where "and" would make more sense, or vice-versa. Surely that could be improved by such an approach?