At least in C++ there's also the matter that the type switching happens at compile time, not runtime. You get a new instance of the function for each type that it's called with.

That's why C++ libraries with generic interfaces need to have their full implementations in the header or else have explicit instantiations for known supported types. If you compile the library first and the project later, there's no way of knowing at library-compile-time which instantiations of the generic will later be needed, and like, the types might not even exist yet at that point.