"Type hints" and "annotations" aren't the same thing.  And type hints are more opinionated about the values of annotations than would be appropriate for the inspect module.  For example, typing.get_type_hints() wraps strings with ForwardRef, turns None into NoneType, and it ignores objects with a "__no_type_check__" attribute.

So, I think it might be okay to *add* a *new* function to the typing module that was equivalent to inspect.signature() (and typing.signature() seems like a good name here).  I don't use type hints, so I don't have a strong opinion on that either way.  But you definitely shouldn't modify inspect.signature() so it produces type hints.