It's not just about limiting nukes to allies, but not introducing nukes to other regional power conflicts. Case in point is both North Korea and Iran. Right now, much of the region around North Korea operates under the nuclear umbrella of the United States. That allows them to relax any nuclear ambitions knowing that they have a deterrent. Same with Iran and other countries, chiefly Saudi Arabia. There gets more complicated, since Israel's nukes give Iran a legitimate defensive reason to want nuclear weapons.