It is a substitute for those unit tests that are essentially checking type invariants. It is not a substitute for all unit tests, but I don't think anyone made (much less intended to make) that claim anywhere in this thread.

"They only tell you that you are matching function signatures correctly."

All of computation can be expressed as application of functions, so for sufficiently expressive function signatures that's not much of a limitation. Of course, if you want to guarantee that your compiles terminate, you need to apply some limits to the expressiveness of your function signatures... but there are powerful guarantees you can get out of even so simplistic a type system as C's, if you work with it rather than against it.