I don't trust anyone with nuclear weapons. It would be lovely if nobody had them. That's realistically not possible right now. As long as countries continue to amass them, there's a need for "more good" countries to keep them. These are almost always democracies.
Democracy is generally speaking just safer and better than dictatorship. I'm just going to stop there, and not get into a debate right now of democracy vs dictatorship.
Would you rather have the good man with the power, or the bad man? That's the ultimate question simplified. You want the good man with the power, then it's a question of who is good, which would lead to huge endless debate right now.
Nuclear weapons have kept the large powers from direct confrontation since the 50's, their existence has saved more lives than their use has cost. As long as they are not acquired by (in our eyes) irrational or suicidal actors they can be used for this purpose. As to whether a nuclear armed Iran would use them as a deterrent or otherwise - which includes providing nuclear weapons to third parties for use against common enemies - I can only guess. My guess is that a weakened theocracy - which is what Iran is - is an irrational actor and with that not to be trusted to "do the right thing".
Yes, that's what we were told. But, was it really necessary to bomb Japanese cities to show them force?
Or alternatively, what makes democratic nations the better shepards of nuclear weapons? It's not like they're asking their voters before they'd start a nuke.
I think the cold war showed us how easy it is to succumb to fear and how close we can get to nuclear annihilation.