I'd sort of invert that and say it's better to use LLMs to just generate tons more test cases for the SQL DBs. Theoretically we could use LLMs to create 100s of Thousands (unlimited really) of test cases for any SQL system, where you could pretty much certify the entire SQL capability. Maybe such a standardized test suite already exists, but it was probably written by humans.
At that point, you'd get a ton more value from doing Property Testing (+ get up and running faster, with less costs).
If I'd had to have either code or tests generated by a LLM, I'd manually write the test cases with a well-thought out API for whatever I test, then have the LLM write tests that implements what I thought up, rather than the opposite which sounds like a slow and painful death.
I hadn't heard of "Property Testing" if that's a sort of term of art. I'll look into it. Anyway, yeah in TDD it's hard to say which part deserves more human scrutiny the tests or the implementations.
Are you sure that LLMs, because of their probabilistic nature, would not bias against certain edge cases. Sure, LLMs can be used to great effect to write many tests for normal usage patterns, which is valuable for sure. But I'd still prefer my edge cases handled by humans where possible.
I'm not sure if LLMs would do better or worse at edge cases, but I agree humans WOULD need to study the edge case tests, like you said. Very good point. Interestingly though LLMs might help identify more edge cases us humans didn't see.