You know what? You're right! But God HAS already done this through Jesus and His sacrifice on the Cross. But you must believe, and you must choose to follow Him in order to understand or appreciate it. In this way -being a part of Christ - you are dead to sin, and have new life. Otherwise you remain as dead in your sin. You might feel alive, but spiritually you're dead.
And to answer another question, before it's asked again, the reason Christians still sin is because it's a process. That's why Jesus says to us to take up our own crosses. Even though you're reborn through Him, the old person still remains, and we must sacrifice that by turning away from sin and temptation everyday, and putting to death the old man. But here's the great thing. He helps us. It's a living relationship, and He is patient. The most loving parent you can even think of is no match for the Love of God.