And if you're really dead-set on paying nondeterminism to get more coverage, property-based testing has existed for a long time and has a comparatively solid track record.
Seems of dubious value as unit tests. LLMs don't seem to be quite smart enough for that in my experience, unless your bugs are really as trivial as adding instead of multiplying, in which case god help you.
I have the toughest time trying to communicate why f(x) should equal f(x) in the general case.
Maybe the non-determinism can be reduced by caching: Just reevaluate the spec if the code actually changes?
I think there are also other problems (inlining a verbal description makes the codebase verbose, writing a precise, non-ambiguous verbal description might be more work than writing unit tests)
That would be good anyway to keep the costs reasonable.