I do promote TDD, but it's hard to convince yourself (or managers) that you need to spend a couple of hours to fix issues regarding the test suite(s) and not the actual product. Those problems are rare, but they do happen. Just my two cents.

Tests is additional code, additional layer and cognitive load to manage. If you iterate in the velocity I think you would in a startup, then a test suite might be a hindrance.

I consider doing a lean startup/product very much like a feature spike - once you've settled THEN you can start writing tests.