I can imagine deleting products may be failing due to some UI change. Maybe a button isn't visible in certain IE versions. Maybe the JS code executing the backend request is failing in some browsers. That's where e2e tests are useful.
Those are purely failures in the UI layer. To the extent that "unit testing" a web frontend is possible, you could catch those problems with a pure unit test that mocked out the backend, it wouldn't have to be an end-to-end test.
