A theoretically perfect next token prediction machine is just an LLM with a temperature of 0, which performs worse than one with a non-zero temperature (i.e. imperfection)

The "prediction" has nothing to do with predicting the future, it just means choosing the most likely next token for existing human text

No that would be a pretty terrible next token predictor. It would perfectly match the training data, but the training data is just a sample of what we are really trying to predict: human language, knowledge, and thinking, which is inherently probabilistic. Perfectly matching the training data is a pretty good sign that you've overfit.