The test can show intended use, show interesting corner cases, and I know it is up to date because it is constantly running and passing.
I think that is a huge underrated benefit of adding a lot more testing.
If I think a developer is going to ask a question of how something works, or about a corner case, isn't that deserving of a test, so they can just see proof of the answer to their question immediately rather than trying to re-derive it?