As horrible as nuclear weapons are, and as ideal as a world without them would be, this is wishful thinking at its best. The level of trust and cooperation required for everyone to give up nuclear weapons is in large part simply impossible given the current state of human and world affairs. We've certainly not managed to eliminate war or armed conflict. All we've done is limit its scope and size.
And speaking of that, it's in large part due to nuclear weapons that there have been no major wars in the past 70 years. The most we've seen were proxy wars that were limited in scope, and while many of those were horrible, they pale in comparison to the two World Wars, or really any of the major power conflicts that preceded them. The world with nuclear-armed major powers is paradoxically MORE peaceful than the world before it was. Prior to the nuclear age, it's difficult to go more than 20-30 years without two or more major powers going to war. The presence of nuclear weapons was the final thing that made "Total War" too costly a concept for rational actors to even consider it.
Reduce their number and scope? Sure, by all means. Get rid of them entirely? That's quite a different thing.
No major wars in the past 70 years? Wtf have you been smoking? We've been in a proxy war with Russia since basically the end of WWII. We've invaded practically every country in the middle east, South America and most of Asia. Millions of people are dead. Basically the entire middle east is at war with us in one way or another as we speak. The only difference between now and WWII is the iron grip our leaders now have on the message our media feeds us. We are in the middle of a world war right now, and have been this entire time.
After memorial day I read an article about how Obama was celebrating the first memorial day without "boots on the ground" in 7 years or something. Meanwhile we've got special forces in every country in the middle east, bombers flying daily missions, drones bombing weddings. Just how gullible are we?!?!