Good question. Answers will be opinion-based, of course, but hopefuly they are based on actual real-world experience.
In my case, I've written thousands of JUnit/TestNG tests over the years, and I happen to develop an advanced testing library (mocking + code coverage + integration testing) for Java.
So, IMO, it's not needed and not productive to write unit tests when you already have a good integration test suite.
Integration tests do take longer to run, of course, but they should still be fast enough that a developer is not discouraged from running them. This is what matters: if the developer can still productively run one test, one test class, etc. when developing new code or modifications, then it's fine. So, avoid integration testing approaches (eg, Selenium) that make test execution too slow/painful.
Another criticism made against integration tests is that they make it harder to figure out the root cause of a test failure. This is not a big enough issue in practice, though.
Martin Fowler makes these same two points in his Unit Test article.