That's precisely what I did in the beginning of my career. To test every method and mock all the dependencies. This had the impact, because we usually don't use a dependency injection framework, that I had to add an interface for almost every class, adding factories with interfaces almost everywhere and then write tests which expect certain method calls and to basically debug the tests while writing them until all calls have been mocked. Thus, whenever I changed the production code I had to change the test as well.

IMHO in my own projects I tend to write tests which test certain parts of a system as well as some dependencies. So usually I'd say they are integration tests instead of unit tests. But I can refactor stuff and once I break something it's usually detected by one of the tests. Maybe unit tests should test for certain cases border cases, which are hard to test with integration tests.