It wasn't that sucky for New Zealand, but we weren't independent... it was rather sucky for a number of other countries, however, namely France... (not that it was overly great either way for France...).
The Alternative to war for WW1 was no war. If the Austian-Hugarian officals had accepted that the assassination of Archduke Ferdinand had been the act of a single man, rather than iccorrectly placing the blame on the Serbian Government then there would have been no war. However because they believed what was nothing but a Conspiracy Theory (that the group that Gavrilo Princip belonged to was supported and finaced by the Serbian Government and that they had ordered it) and even when Serbia agreed to most of the terms that was demanded (unreasonably) of it, still forced the issue to war, it never would have happened, and 8 million linves would not have been extingushed. (Who says that Conspriacy theories aren't dangerous?)
I disagree that wars post WWI have had their roots in WWI however, with the obvious exception that all history is caused by all history before it...
WWII/Europe - Occurs due to the treatment of Germany, the forced payments of restitution resulting in the bankrupting of its economy and the removal of its most productive lands. This allows the Nationalists to gain a foothold in the Government and ultimately Hitler's raise to power through promises to restore Germany.
WWII/Pacific - China refused to sign a peace deal which included Japan because Japan had taken a strategic area of Chine from the Germans and refused to give it back. England and France said they would support China, but then reneged, leading to later hostilities between Japan and China and starting WWII in the Pacific.
Israel's Wars - Has fought several wars, all tracing their roots back to the "liberation" of Palastine in 1917, the British rule (1922) and then the formal creation of the State of Israel in 1946.
India/Pakistan - Requested Independence from Britain after their part in WW1, and was denied. Ghandi tried again in 1921 and failed. Finally granted after WWII, with the british leaving and war betwen Hindu and Muslim leading to the the spliting of India into India, Pakistan, Bangladesh (East Pakistan) and Kashmir.
Vietnam - Had requested independence as a reward for their part in the Asian side of WW1. The French denied it, but over the following years and especially after WWII, that movement grew until it became a war in the mid 1950's to remove the French, which lead to US involvement in 1964.
Gulf War 2 and 3 - The border of Kuwait and Iraq was never settled when the Ottoman Empire was broken up, it was this border disute and Iraq's refusal to see Kuwait as a soverign nation that caused the '91 Gulf War, which lead to the current one.
Bosnia/Serbia/Yugosalvia - A direct consequence of the creation of a country by shoving people together after the dismantalling of the Austro-Hungarian Empire.
9-11/Afghanistan - Has its roots very much in the destruction of the Ottoman Empire and OBL's desire to remove western influence over the Islamic Countries and restore the Great Islamic Empire.
Did I miss any? About the only one that isn't tracable, that I can tell is the Korean War.