Why does it need to be based on the mass of an arbitrary molecule? Can't it just be 10^23 or 10^24? Most of the time, you're going to have to look up constants

Why does it need to be based on the mass of an arbitrary molecule? Can't it just be 10^23 or 10^24? Most of the time, you're going to have to look up constants to convert moles to mass anyways.