Most of the real world is about manipulating the real world. For algorithms it is fine to say depend on the pure inputs/outputs. However what we care about is that global state is manipulated correctly and so the integration tests that verify that are what are important. In most cases your algorithm shouldn't be unit tested separately since it is only used in one place and changes when the users change: there is no point in extra tests. If the algorithm is used in many places comprehensive unit tests are important, but they get in the way when the algorithm is used only once and so the tests just inhibit changes to the algorithm as requirements change (you have to change the user, the integration tests, and the unit tests that are redundant).

As such I disagree. Global state is what you should be testing - but you need to be smart about it. How you setup and verify global state matters. Don't confuse global state above with global state of variables, I mean the external state of the program before and after, which means network, file, time, and other IO things.

IO and global state is also just inputs that can be part of arrange-act-assert. Instead of mocking your database call to always return "foo" when the word "SELECT" is in the query, insert a real "foo" in a real test database and perform a real query.

Again I've heard "but what if my database/table changes so rapidly that I need the mock so I don't need to change the query all the time", in which case you ought to take a moment to write down what you're trying to accomplish, rather than using mocks to pave over poor architectural decisions. Eventually, the query fails and the mock succeeds, because they were completely unrelated.

So far I've only seen mocks fail eventually and mysteriously. With setups and DI you can treat things mostly as a black box from a testing point of view, but when mocks are involved you need surgical precision to hit the right target at the right time.