True, but when nukes are developed then a 'big' War is something no one will want.
Remember nukes development was for the USA a priority in OTL because such a powerful weapon could win the war and make the allies take less casualties. If there is no need for them, or more precisely no push for having them as fast as possible, why would they invest the huge amounts of money needed to develop them as in OTL?
And also, you are ignoring some of the issues that were screaming for a World War.
-First you have communications, they were really improving, and what happened in the other side of the world could be known really fast.
-Then you have economics. Germany was growing really fast, and the UK didn't like this. They were eager to limit their growing power, and their fleet too, which was a direct threat to Royal Navy.
-Also, there is French Revanchism, they want to take back Alsace-Lorraine.
-There is also the Balkans, which is a gunpowder barrel about to explode. European Great Powers have interests there, and they will defend them.
-Russia was also eager to gain prestige and grow their influence. They needed to show their people that they were really good and powerful, so Revolution could be avoided.
-The USA was growing really fast and becoming a Major Player, and they wanted to prove that. They needed prestige, and that's something your earn fighting. So they would likely intervene somewhere they have some interest,or where they see an opportunity.
-Japan aslo wanted to expand.
-Most European powers had colonies, so if there was going to be war between them, at least some fight would happen in the colonies.
And I could go on with many more reasons. There was a delicate equilibrium
which could be broken really easy. And there more this equilibrium takes to fall, the more likely it would do.