You don't test inner functions the same way as you don't test private methods in a class. You only test for public API. They are implicitly tested when you test the higher level function.
Typically I would agree with you, but I've worked on a lot of old codebases with extensive testing for deep scary private parts. A good example is some public method which does something seemingly innocent and useful, but in its guts calls a bunch of black magic to deal with different operating systems and configuration options.