I'm not quite sure what the author is arguing for here in particular.
Anything that makes writing tests a bit easier, e.g. suggestions for additional test cases, would be cool, but ultimately tests are about writing down your assumptions/expectations about the code.
No, they are not formal proofs and sometimes they are not perfect but they still provide a lot of value. So far I haven't found a good reason not to write tests (since I outgrew my newcomer attitude) and yeah integration tests are usually what I focus on most. For any case where testing whole systems today is hard, there are some fundamental challenges (e.g. end to end web UI test). I don't quite see how tooling will get rid of the need for tests.