The whole western world sat and watched two decades of persecution that Armenians suffered which ended up becoming a genocide, even Russia who declared herself the protector of Ottoman Orthodox christians didn't move a finger. And those who managed to flee the country were not always welcome. See e.g. the autobiographical movie Mayrig.
Also, in 1915 when the Armenian genocide started, the western world was already locked in a bitter war with the Ottoman Empire. Did you want the infantry sent against Ottoman positions to be carrying banners saying "Okay, now we really mean it!"? Then after the war you had the major players exhausted, denuded of men, materials, and war chest.
Finally, there wasn't really a concept of a 'world cop' like there is in the Pax Americana... but even with the Pax Americana, there's plenty of places it ignores (eg see the five-year Second Congo War, ended this century, 5 million dead).
This picture that you're painting skips an incredible amount of context.
The Ottoman Empire was a world power up until the first world war - suggesting that other world powers should go to war against them because of how they treat people in their own sphere of influence is completely missing the context of the times.
Hell, it's even missing the context of the current times - how many western nations intervened in the annexing and oppression of the Crimean peninsula by Russia? What is the World Cop doing about the clear oppression of Tibetans by China? What is anyone doing about the plight of North Koreans under their murderous dictatorship? What about the Khmer Rouge in the 70s, where the World Cop actually backed the people doing the genocide?
Context is important.