It also has no good definition for its semantics when presented with a NaN.

You would use a partial ordering: https://en.cppreference.com/w/cpp/utility/compare/partial_or...

How would that apply to Fortran’s arithmetic IF statement? It goes to one label for a negative value, or to a second label for a zero, or to a third label for positive. A NaN is in none of these categories.

I mean maybe I'm missing something but it seems like it behaves exactly the same way as subtraction? At least for integers it's definitely the same, for floats I imagine it might handle equals better?

C++ has operator overloading, so you can define the spaceship for any class, and get every comparison operator from the fallback definitions, which use `<=>` in some obvious ways.