What is the main benefit of storing all nuclear waste at a single site

The main benefit of this would be that the nuclear waste security can check and monitor the hazardous materials.

If you were to just throw it all over the place, then there would be radioactive waste all over the world and people would get sick, not to mention the damage it'd do to the environment. By keeping it all in one place, they can contain it and prevent it from harming the environment (well, at least the rest of the environment) and people.