Because it's not calibrated to. In LLMs, next token probabilities are calibrated: the training loss drives it to be accurate. Likewise in typical classification models for images or w/e else. It's not beyond possibility to train a model to give confidence values.

But the second-order 'confidence as a symbolic sequence in the stream' is only (very) vaguely tied to this. Numbers-as-symbols are of different kind to numbers-as-next-token-probabilities. I don't doubt there is _some_ relation, but it's too much inferential distance away and thus worth almost nothing.

With that said, nothing really stops you from finetuning an LLM to produce accurately calibrated confidence values as symbols in the token stream. But you have to actually do that, it doesn't come for free by default.