Obviously, tests are a good thing and they are an important part of QA. I'm not arguing against automated tests.
I'm merely trying to point out a weakness in the practice of "test driven development", where you write tests before you implement the functionality.
Since you already have tests while you work, it's really easy to just treat them as a checklist, and once all tests pass it feels like you are done.
But in reality, once the feature is done, that's when the hard QA work starts. You need to review the code, make sure you considered all error conditions, check if your assumptions hold throughout the execution of the program, ensure that your code is resilient to unexpected user input, etc.
TDD might be a valuable part of a development/QA workflow, but just introducing TDD on its own is not going to make your product any better.