It’s funny that in your paragraph there I thought you were about to write… “for that reason alone, TDD is the only way that makes sense to me.”
The reason is, the tests and the code are symbiotic, your tests prove the code works and your code proves the tests are correct. TDD guarantees you always have both of those parts. But granted it is not the only way to get those 2 parts.
You can still throw into the mix times when a bug is present, and it is this symbiotic relationship that helps you find the bug fast, change the test to exercise the newly discovered desired behaviour, see the test go red for the correct reason and then make the code tweak to pass the test (and see all the other tests still pass).
The reason is, the tests and the code are symbiotic, your tests prove the code works and your code proves the tests are correct. TDD guarantees you always have both of those parts. But granted it is not the only way to get those 2 parts.
You can still throw into the mix times when a bug is present, and it is this symbiotic relationship that helps you find the bug fast, change the test to exercise the newly discovered desired behaviour, see the test go red for the correct reason and then make the code tweak to pass the test (and see all the other tests still pass).