Earlier quoted context omitted.
The more independent entities with Nuclear weapons, the more avenues for one to be used. Simple as that. Every country has potential to move towards national fanaticism over time.
That's just not the case. Look at every conflict of the past 50 years. Major powers trade very carefully against a nuclear armed nation. Which by the way largely explained Biden's tepid military support to Ukraine, giving them just enough weapons for them not to collapse but not enough to make any serious dent to Russia. And basically maximising casualties by making the conflict last.
I too hope that more nuclear arms will result in reduced conflicts and a reduced risk model overall. But if I were to bet, I'd bet that if we 10x the number of players with Nuke's, we 10x the number of chances for some to be used.