If God isn't concerned about us, or if He isn't able to do anything about the evils in our world, then yes, it is useless to pray for world peace (or anything else, for that matter).
But God isn't like this! God loves us and is deeply concerned about the evils we face. Furthermore, He is all-powerful and is able to do something about them. This is why we can expect Him to answer our prayers according to His perfect will, including our prayers for peace among the nations (and everything else that concerns us). Centuries ago, the prophet Isaiah declared, "Surely the arm of the Lord is not too short to save, nor his ear too dull to hear" (Isaiah 59:1).
Does this mean all evils would vanish if we just prayed hard enough? No it doesn't, because evil is still real, and Satan is still at work. Only when Christ comes again and Satan's power is broken will the world know true and lasting peace. But in the meantime, God commands us to pray for "all those in authority, that we may live peaceful and quiet lives in all godliness and holiness" (1 Timothy 2:2).
Today millions are celebrating the annual National Day of Prayer. Take time today -- and every day -- to pray for our nation and its leaders. God is still at work, whether we realize it or not. And some day He will bring about "a new heaven and a new earth, where righteousness dwells" (2 Peter 3:13).