Why define functions with the empty domain? (specifically in primitive recursion)

Question

A function can have an empty domain, as long as the range is not empty, as this satisfies the conditions of existence and uniqueness of images. However such a function can never be called, as there is no value in the empty set to pass to it. Primitive recursion defines some functions to be $\mathbb{N}_0^k \to \mathbb{N}_0$ with $k \in \mathbb{N}_0$. Thus it defines a function $\emptyset \to \mathbb{N}$. But what for? That function is impossible to ever call. What is the rational behind defining such uncallable functions?