Healing is built into out bodies by God so, how it is activated isn't really the issue.
The question, I think is funny is this, why ask God to heal when Jesus told believers to heal?
Mat_10:8 Heal the sick, cleanse the lepers, raise the dead, cast out devils: freely ye have received, freely give.
As a matter of fact, for those of you like research, you can't find a SINGLE instance in the New Testament (I know you don't read it, but you can Google it) where ANY New Testament believers are directed to ASK GOD to heal anyone. gasp. shock.
The central question of this website comes from a fallacy, that most Christians, unfortunately, believe and agnostics / atheists seize upon, God does NOT initiate healing, WE DO. I could get into the silliness of Calvinism, but much of what I read here is your opposition to Calvinism, not any actual true Christian doctrine.
Jesus was the SON OF MAN, so he was a man (If you care to acknowledge his existence). But as a man, he NEVER prayed and ask GOD to heal anyone HE (Jesus) healed them as a man knowing how to use the power he was given.
And, to lay this to rest, he did heal the maimed (missing body parts, amputees, or whatever you want to call them)
Mat_15:30 And great multitudes came unto him, having with them those that were lame, blind, dumb, maimed, and many others, and cast them down at Jesus' feet; and he healed them:
I can expound much further on this, if you like, but the concept of asking God to heal isn't scriptural, nor is it Christian, WE are to heal.
If you are following my logic, I would be glad to explain healing, faith healing, etc, but I find this supposedly impossible question a lesson in ignorance. Why? It isn't scriptural nor Christian, to pray and ASK God to heal, you can't find any examples of it in the New Testament. Healing lies on shoulders of the believer, not God.
Case in point, when Jesus walked this earth, on over dozen occasions HE HEALED THEM ALL, not God. I am not arguing against his deity, but for a very specific reason, Jesus (God) came as a MAN using the power of God inherent in men
So, to sum up my points.
Atheist: Well, let's pray and ask God to heal this amputee
Christian: Why don't we heal him, that's what Jesus told us to do, not just pray for him.
Atheist: You don't want to pray for God to heal this amputee?
Christian: No, there is need to pray for God to heal, let's use the power God put in us to heal this amputee
Atheist: blah, blah, blah
Christian: Yada,Yada, Yada, Yada
I don't know, I thought the above discourse sounded funny in my head, but you get the point.
Once again, the mechanics of HOW to get him (the amputee) healed via the supernatural power of God that rests in us is up for debate, but you truly misunderstand why GOD became a man in the first place. You simply don't understand Christianity at the core.
If God had permission to do everything he wanted to do in the first place, why go through the trouble of becoming a man? You simply don't know God, nor do you know who is really in charge of this earth.
Psa 115:16 The heaven, even the heavens, are the LORD'S: but the earth hath he given to the children of men.