Code needs to be tested. Sometimes that testing is best done by an algorithm.
We recently had a user story that involved removing particular characters from the application number string. The purpose was to address a readability issues - at a glance certain characters and numbers are indistinguishable, so removing the offending characters from the string they were generated from. A simple enough coding exercise.
This card, however, sat in the testing column for a long while. It didn't need to, as we had built a unit test that did what a regular tester would do - throw lots of data at the generation and see whether those offending characters were present.
An automated test, in this case, could do what a human could not: quickly generate and accurately assess the functionality. It's checked 1000 times every time the code is compiled - overkill as far as what's needed to be tested, but that overkill is computationally negligible.
Writing the unit test first (TDD) gives the developer the target to aim for, as well as creating the before and after test artefacts. At the very least, the unit tests results could supplement the functional spot-checking that would constitute normal testing for such a story.
Writing code that verifies functionality is not simply for helping developers to write better code, but can be the best tool at the disposal of the testers for doing testing. It's leveraging technology at tasks it excels, which is what we ought to be using technology for.