But isn't the real problem that you cannot be sure that the other side have actually disarmed. So there is this incentive to build and or keep nuclear weapons

But isn't the real problem that you cannot be sure that the other side have actually disarmed. So there is this incentive to build and or keep nuclear weapons in secret - just in case. Then you have this outcome where both sides still have nuclear weapons, but not publicly so that it is no longer a deterrence but a a pure offensive weapon.