Unit tests test that the units do what they are supposed to do. Functional tests test that parts of the system do what it's supposed to do.
If you change the implementation for a unit, a small piece of code, then the unit test doesn't change; it continues to test that the unit does what it's supposed to do, regardless of the implementation.
If you change what the units are, like in a major refactor, then it makes sense that you would need whole new unit tests. If you have a unit test that makes sure your sort function works and you change the implementation of your sort, your unit test will help. If you change your system so that you no longer need a sort, then that unit test is no longer useful.
I don't see why the fact that a unit test is limited in scope as to what it tests makes it useless.
If you change the implementation for a unit, a small piece of code, then the unit test doesn't change; it continues to test that the unit does what it's supposed to do, regardless of the implementation.
If you change what the units are, like in a major refactor, then it makes sense that you would need whole new unit tests. If you have a unit test that makes sure your sort function works and you change the implementation of your sort, your unit test will help. If you change your system so that you no longer need a sort, then that unit test is no longer useful.
I don't see why the fact that a unit test is limited in scope as to what it tests makes it useless.