I agree with you partially. I just want to argue there are several factors that lead to this perverse behavior.
Empirically:
Use web gpt-5-instant in TEMPORARY mode. If you ask for "igloo emoji" it confidently (but ONLY in temporary mode) says that "Yes, igloo emoji is in Unicode 12 and is [house-emoji ice-emoji]." Then it basically stops. But it has satisfied its condition of confidently expressing its false knowledge. (Igloo emoji doesn't exist. gpt-5-instant in non-temporary mode says no. This is also weird because it suggests the temporary mode system prompt is laxer or different.)
The mechanism you describe partially explains why "seahorse emoji" leads to babbling: As it outputs the next token, it realizes that the explanation would be worse off it if next emits stop token, so instead it apologizes and attempts to repair. And cannot satisfy its condition of expressing something confidently.
The upstream failure is poor knowledge. That combined with being tuned to be helpful and explanatory, and having no grounding (e.g. websearch) forces it to continue. Finally, the token distance from the manifold is the final piece of the puzzle in this unholy pathological brew.
You're incorrect that statistical language modeling is "post-hoc", it's rather "pre-hoc" / "pre-hack". Most foundational works in language modeling started as pure statistical models (for example, classic ngram models and Bengio's original neural language model from 2003), and it was later that hacks got introduced that removed statistical properties but actually just worked (Collobert and Weston 2008, as influenced by Bottou and LeCun). Where I agree with you is that we should have done away with the statistical story long ago. LeCun's been on about energy-based models forever. Even on HN last week, punters criticize him that JEPA hasn't had impact yet, as if he were behind the curve instead of way ahead of it.
People like statistical stories but, similarly to you, I also think they are a distraction.