even though you don't know that the deleted file no longer served any purpose, the tests know it.

Yes, if you solve the Chesterton fence of figuring out why certain tests are in the suite to begin with. Certainly an easier task than with the actual code, but still a task. I recall removing failed (and poorly documented) unit and integration tests I myself put in a couple of years earlier without quite recalling why I thought it was a valid test case.