His quote was only relevant to preventing other nations from obtaining nuclear weapons. While for now nuclear peace still exists it still remains to be seen in the long term, especially as more and more nations think of developing nuclear weapons, whether the idea of allowing nuclear proliferation was a good one in the end.
I'm pessimistic here. The countries that once pursued/had nuclear weapons, but then signed treaties and gave up on them were screwed one after another: Iraq, Lybia, Iran and now Ukraine. Contrast with North Korea, that pursued them not matter what. Nobody ever screwed them. The failure of the great powers in keep their word with countries that actually took measures to stop or limit nuclear proliferation will seriously backfire.
Yes they were screwed and lots of people did die unnecessarily. However, Saudi Arabia wants nukes, Shinzo Abe (ex Japan PM) said Japan should get nukes, the future of the long term program of Iran is still unsettled. Apartheid South Africa had nukes and only gave them up because they didn't want the native Africans to have them. The problem becomes as more and more countries develop nuclear weapons, the risk of conflict using them grows higher. Already we have a long term conflict between Pakistan and India where both nations are nuclear armed and I very much doubt Pakistan's nuclear security as anywhere as good as say America's or China's. What would happen if 20 or 30 or 40 countries had nukes? They would threaten to use them over every small thing and eventually I guess someone would use them, and who knows what happens then.
Or when the actors are no longer nations modeled on an individual decision-maker but, eg trucker convoys purchasing their way into the club.