> It's a spiral, the moment you allow a nuclear power to use that status to force the hand of an opposing nation at war you open a can of worms. Since 1945 the world has been trying to control proliferation through other means, wars of annexation have been shunned, you really don't want that to come back into a world armed with nuclear weapons.
You also have an example of what happens when some countries are more powerful than others: the veto at the UN Security Council. The UN is essentially unable to do anything that is against the interest of US, Russia or China (it just happens that France and the United Kingdom usually agree with the US). Imagine US, Russia and China having the same power but with 1) the actual ability to wipe enemies off Earth, instead of just blocking UN processes; 2) anybody able to join the club "just" by investing into nuclear proliferation. Doesn't seem good.
Do not discount the veto at the UN of the UK and France. Part of the current situation with Israel rests on those two countries colluding with Israel for a war the other three did not want.