> This pretty much never comes up

I regularly use that in C, to make sure a function matches an abstract interface. Sure, that often ends up in a function pointer, but not always and when I declare the type signature, it isn't yet a function pointer.

> but not define

I think that is because the type signature only contains the types, but no parameter names, which are required for a definition. This is arbitrary, since for data types, the member names are part of the type. It sounds totally fixable, but then you either have two types of function types, one where all parameter names are qualified and one where they aren't and only could use the former for function definitions. Or you would make names also mandatory for function declarations.