It's not a hack to create a new set and work out rules for how to use it which are both internally consistent and support easy morphisms with more familiar sets.

It may not be easy, but it's hardly a hack. It's one of the big ways math works, really. Are negative numbers a hack? Rational numbers? Algebraic numbers? Well then neither is the two-point compactification of the reals or extending the natural numbers into the ordinal numbers.

These are things with very precise models and interpretations. No hacks at all.