The discussion is basically: what is a model trying to do?

One may reasonably assert it isn't trying to do anything. But, in practice, if you give it an objective function and optimize it, the model is basically trained to "do" something. So what is it trained to "do"? During pre training it is trained to produce a distribution which is a prediction of the next token in it's training data samples. During RLVR and RLHF, it is trained to produce a distribution of tokens that will maximize a scoring function over many steps - not just the next step. The fact that it produces a distribution of potential choices for the next step doesn't mean the next step is a prediction. It's more of a "strategy" or "probabilistic path choice". The word used in RL is a "policy". It's a decent word to describe what the model is.

So, modern LLMs are trying to produce a good sequence of tokens. They are "good token sequence producer machines". Not "next token prediction machines". Pre RLHF (in practice, go back to pre chatgpt) they really were "next token prediction machines".