For one thing, many have wept for the fall of Austria-Hungary. It was not the perfect one, but a good option IF IT COULD transform into multinational federation. You may cry about being a prison of nations, and yet most of population was happy until the WWI, and THEN the distress was caused by the war, not primarily by the existence of Empire.
On the other hand, multinational or national empires, make no difference. Wars are being waged by both of them, and in greater meaning, war WOULD come anyway. There were just too many small and great wrongdoings on all sides.
Calgacus & HurganPL: Idea of national state comes with the French revolution earliest. Until then, it wasn't national or multinational states. Yes people identified with groups, but unlike today, it was more ethnic. Just two examples: in Middle ages, many times a country or land changed rulers often. But people's loyalities were not to the "nation" nor country, rather they were to their respective Lord, and the nobility was loyal either to itself or the ruling House. Uprisings of common people then, were not motivated by national ideas, but a desire for better life.
Another example: Roman empire (I'm talking about early Empire). It consisted of many ethnic groups ( I use the term ethnic rather than nations, as the very term of nation was not used then). Romans called themselves "people of Rome". Social and political status was different not by nationality, rather by birth, or wealth, or freedom. Slaves could work to their freedom, barbarian mercenaries or cities and groups could gain the status of Roman Citizen. Roman Empire was multi-ethnic, multi-religion, multi-whatever-you-like, but NOT a multinational.
And I can give you an idea of multinational state going to hell... Yugoslavia. Before WW2, large dominated by Serbs, after then, national problems were mostly held under carpet by Tito and Communist party. Once Tito gone, the problems started to reappear again, and after not more than 10 years not even communist party was united. What followed we all know. Another round of Balcan wars.