> The moment you let the LLM write the tests without understanding them, you may as well just let it write the code directly.

I disagree. Having tests (even if the LLM wrote them itself!) gives the model some grounding, and exposes some of its inconsistencies. LLMs are not logically-omniscient; they can "change their minds" (next-token probabilities) when confronted with evidence (e.g. test failure messages). Chain-of-thought allows more computation to happen; but it doesn't give the model any extra evidence (i.e. Shannon information; outcomes that are surprising, given its prior probabilities).