I agree that you would want them to be different types; otherwise you would just use an unscoped enum. But that implies that if you write…

  /* example.h */
  void f(enum struct { x, y } arg);

  /* example.c */
  void f(enum struct { x, y } arg) {
    /* do something with arg */
  }

…then you've just created a function with two different overloadings based on distinct anonymous types which just happen to be spelled the same way. Without a type name I don't see any way you could define a function whose prototype would be compatible with the forward declaration. You also have conflicting definitions of "x" and "y" with the same names and scope but different types. Perhaps with GNU extensions you could use typeof(x) for the argument and avoid the conflict, but that isn't standard C++.