The primary, number one benefit is peace. Great power war on the European continent has not happened in over 70 years. This is a big deal. Prior to the Second World War, great power war in Europe was not an uncommon occurrence. The continent never really want more than a decade or two without a flare-up between great powers that left a hundred thousand or more (sometimes many, many more) people killed. We are living in the middle of a historic period of peace between great European powers that is unrivaled in history. I would argue that the primary reason for that is because nearly every European power is cemented in a mutually beneficial military alliance. Each is responsible for the security of the collective. The existence, strength, and longevity of this bond means that there is no incentive for such conflict to happen, and as such competition between powers is channeled into other avenues. The alliance has removed the need to compete militarily with other powers, and instead allowed a degree of integration and cooperation that is unprecedented in history.
This is important because the entire world benefits from peace. It improves cultural ties, economic ties, and trade. These things in turn lead to greater wealth, prosperity, and increased standard of living . War and military competition are inherently destructive. The world is a better place when those things don't happen. Europe is singled out because of the concentration of a large number of great powers in one continent, the size of its economy and trade (which give it great influence over the world economy), and its (pre-1945) history of conflict.
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