I find some of the most interesting, and catastrophic failures in my agent fine-tuning come from the clamping down of non-determinism. It is totally the correct approach, but must be handled delicately. The non-deterministic core remains, but now under bimodal pressure.
I think stochastic parroting is really a very accurate description of what they do (if underserving of the overall usefulness of LLMs). As long as you consider they are parroting from the whole of human intelligence. Its just that as they have gotten more sophisticated, the amount of gates, guardrails, and tertiary tools add variety. Trace any LLM hallucination back to provenance and you begin to see how the stochastic parrot works.