God wants to establish his lordship over the cosmos through us. He wants his bride to reign with him (2 Timothy 2.12; Revelation 5.10, 20.6). This was the plan from the beginning (see Genesis 1.26-27). It's not enough to know Satan has been defeated. He has to be routed, to be eradicated, out of our homes, out of our families, out of our lives, and out of our minds.
The best way to accomplish this is through prayer.
The prayer of the righteous is powerful and effective (James 5.16). Prayer moves God and makes an incredible difference in the world. Jesus told us to ask God for things, promising that they would be given (Matthew 7.7, 18.19-20; John 14.13-16, 15.7, 16.23). He encouraged us to pray with tireless persistence as though God needed to be called to attention (Luke 11.5-13, 18.1-8).
In light of this, we have to acknowledge that prayer is an essential part of our co-reigning with him. God's will is like a business check that must be cosigned in order to be validated. The church is the cosigner, and prayer is our signature.