He's bringing about good despise evil and doesn't need it, then why does he allow it? He can stop it. He doesn't need it. It's evil. Sounds to me that you're suggesting that he can't stop it after all.
Evil is a necessary consequence of the moral freedom of created beings. If intelligent beings can choose virtue, they must also have the ability to choose evil, otherwise moral agency becomes meaningless. God wants from us legitimate virtue, which inescapably means giving us the moral freedom to sin.
Natural evil, such as natural disasters, are an unfortunate reality of an imperfect natural world. This state of affairs is a consequence of the fall from grace as described in Genesis. The fall from grace is also the reason for the human propensity towards sin, and the necessity of God's grace in living a moral life.
So why does he allow it if it's something he can and wants to stop?
Asking the same question over and over will get you no where. God is the creator, not a micromanaging puppet master. God allows us to our own choices because he has created us with free will. Freedom necessitates the ability to do evil things. However, God has not excepted us from moral culpability. Every soul will give an account before God for its life here on Earth.
Then moral agency is a greater good, i.e. something more important than stopping evil.
You're actually not that far off. Surely, you can see that virtue when it is a true and free choice is superior to 'virtue' that is compelled by the inability for anything but? Thus creating his intelligent creatures with moral agency is a greater good than creating programmed automatons. Of course, evil has already been utterly conquered by Christ's death and resurrection, but whilst on Earth we must deal with it and strive to overcome it as much as we can. Jesus has provided the means for our justification before God, we have only to accept it and align ourselves with God as much as possible.