Ok. I'm not actually that wedded to the order you do the two operations in. I think there is some value in writing tests first, so that you can verify they fail (before the code is written) and then work (once it is complete). But I think it's less important to do them first than to do them.

IMO, the "killer app" for unit tests is regression testing. If I make a change and the test suite still passes, I can be reasonably sure that I didn't break anything. All the other benefits are "nice to haves" in my mind.