No, none of the combatant states wanted another Great War. You are grossly oversimplifying the factors that led to there being another World War.

Germany wanted to wipe out all the Slavic peoples in Eastern Europe and repopulate the lands with Germans (Generalplan Ost) and regaining it's lost honour from the last war. This meant fighting the Soviets, French, and British.

Japan wanted to mantain a powerblock all around Far East Asia, this meant fighting the Dutch, British, and French. They only attacked the US because they embargoed Japan's purchasing of oil after the latter's invasion of French Indochina. They wanted to quickly strike the US at Pearl Harbour and eliminate their naval capabilities long enough for them to finish off China and have a larger force.

Italy wanted to create a sort of "Neo-Roman Empire" by expanding it's homeland in the Mediterranean and by bolstering the amount of colonies it had. This meant fighting the French, British, and Greeks.

I really don't care about this argument, just that bad history gets on my nerves.