In what world or frame of reference would doing TDD have "little" bearing on output quality? If you build a system around satisfying some set of requirements it seems logical that output quality would have pretty heavy correlation.
It's possible to satisfy a set of requirements with code that's low quality. There's the maintainability of the code, for example, or the performance of the system.
for LLMs, TDD amounts to little more than ceremony. there is a study on this exact topic: https://arxiv.org/pdf/2602.07900