The model does not "output the token that is most likely to come next". The model provides a list of probabilities and the sampler algorithm picks one; those are two different components.
If I put a weight on one side of a die, and I roll it, the die is not more confident that it will land on that side than it would be otherwise, because dice do not have the ability to be confident. Asserting otherwise shows a fundamental misunderstanding of what a die is.
The same is true for LLMs.
But there are algorithms with stopping conditions (Newton-Raphson, gradient descent), and you could say that an answer is "uncertain" if it hasn't run long enough to come up with a good enough answer yet.