Seems to me that asserts are a force multiplier on tests. If you have a bunch of asserts, every test case you write is extra valuable -- you aren't just verify

Seems to me that asserts are a force multiplier on tests. If you have a bunch of asserts, every test case you write is extra valuable -- you aren't just verifying correct input/output behavior, you're also verifying that all asserts held. In the extreme case, I can imagine ditching all your small-scale unit tests for a combination of asserts and end-to-end integration tests.