But if you're having to create lots of mock objects, that's a huge signal that your objects are tightly coupled, and that not only are you writing a bad test, you've written a bad subject-under-test.

Yes, you still have to write integration tests. But the discipline of testing your objects in isolation and outlining the objects they collaborate with is a major benefit of using test doubles, not a downside. If you can't reason about your objects in isolation, how can you expect to reason about them in aggregate?