Shouldn’t everyone have nukes then, for maximum peace?

That's been proposed before btw and game theorists can justify that as being more stable in some ways. However it reduces the power of the incumbents (so why let it happen?) and the odds of having an irrational actor with nukes goes up.

no, only the 'big rational ones', they think carefully.. that why Iran cannot have, and so as NK, but NK is a mistake because they(china,USA...) failed to prevent NK have it.

You want people with a lot to lose in a nuclear war to have nuclear weapons, and to make sure no-one else does.

In theory, yes, because nobody would want to launch first because they'd get obliterated. However, it only takes one country to not be rational.

Nuke-owning countries' leadership seems to have become more and more unhinged and less rational, predictable, or honorable over time. Putin already threatened to use nukes if the conflict they caused themselves crossed their own border. It didn't happen, but the threat was there. The US' leadership is unhinged and irrational. etc.