Prosperity inhibits all war, nuclear or otherwise.
Why would a person who is happy, entertained, wealthy, well fed, and have 200 years of healthy high quality life expected ahead of them going to risk losing what they have in war?
-- there aren't zero reasons, sure-- but there are fewer.
And our technology has brought us absolutely tremendous prosperity in many regards and there is good reason to believe that AI can help create much more.
You do realize that the people currently holding their fingers over the proverbial Big Red Button are some of the wealthiest, most over-privileged people to have ever lived?
'Prosperity' has never been and will never be enough for some people. And unfortunately those are the same kinds of people who relentlessly seek power.