It's a little different than that. Your bundle of nerves and meat is not static. It changes over time.
To me the heart of the "next token predictor" is that the distributions are static. You can manipulate what you feed into it through context (and a lot of interesting engineering has been applied there through CoT and other techniques to manipulate the prompt). But these models as implemented will never be able try things and learn from mistakes or adapt. They are a set of weights frozen in time. A set of distributions derived from the original data that created them.
That's not quite true though. The fact that most models are in practice non-deterministic has been a huge point of contention.
And there's nothing inherently stopping labs from continuously fine-tuning the weights after every new invocation. It's just a difficult (not to mention expensive) software and ML problem.