Why can gravitational potential energy be described as an arbitrary value?
Answer Only changes in potential energy matter. Where you start and where you end are the determining factors in calculating potential difference, not the path taken or the arbitrary starting value. If you calculate a change in potential energy, you end up subtracting arbitrary the initial potential energy from the final potential energy, so if you start with an initial potential energy of arbitrary value, you end up subtracting it in the end. So mathematically there’s no reason to not have the starting potential energy *not* be arbitrary for purposes of any meaningful calculation.
