Agree with you on that. There is nothing about LLMs that makes them uniquely suited for bug finding. However, they could excel re:bugs by recovering traces as you say, and taking it one step further, even recommending fixes.
Correct, what is unique about LLMs is their ability to match an existing tool or practice to a unique problem.
One possibility is crafting (somewhat-)minimal reproductions. There's some work in the FP community to do this via traditional techniques, but they seem quite limited.