I agree we must learn how to pray according to His Will not ours....but healing is always the Will of God.
But, so often, that is our desire because of our own fear of dying.
Let me give two examples: -
Example 1: -
A pastor friend of ours, prayed for a woman who had AIDS and was dying, and God allowed her life to be extended for a period of about three months while she was getting right with God. The woman gave away her idols, but the people she had given her idols to returned them to her because of the "bad luck" that they brought them. The woman had to destroy all of the idols that she owned. Her witness during those three months allowed the Gospel to be preached to her neighbours in a very practical way.
After the three months of her getting right with God, the AIDS took a new hold on her life and she began to die quickly and the pastor took us to her house with him to pray for her to be healed again. He was wanting to demonstrate his power again by healing her but her body was slowly shutting down and he had to release her into God's purposes.
My wife and I had to intervene and quietly and forcibly suggest to the pastor that the prayers that were needed for the woman were prayers of peace and that she would be drawn closer into God's warm embrace and that she, in her death, would be God's witness to her neighbours as she faded away a day or so later.
At her funeral, her witness of her faith was explained to her friends and neighbours and it was a funeral where hope was preached. It become a time of praise and wonder at the working of God in the lives of people.
Example 2: -
My mother suffered an intestinal hemorrhage and was bleeding out. She was 91 years old, my father had passed away a year or so previously, she was now blind and on blood thinners for her heart conditions. The family, my four sisters and myself, knew that it was her time to die as her quality of life was very poor. She was now bed ridden. On the Sunday morning the family gathered at the hospital to be with her and my wife and I had skipped church to be there. We had advised a member of the church family that we would not be able to attend and this was passed onto the pastor of the church. We, as a family, had not asked for any prayers, but the pastor of the church we were attending took it upon himself to take authority to pray for a miracle healing so that she would live. The doctors at the hospital gave her medication to counteract the blood thinners she was on and replaced her blood using 17 bags of blood to help her blood to clot and stop the hemorrhaging. She lived for a further six months but her quality of life was no longer there and she suffered greatly during this time.
The pastor of the church used our situation to demonstrate his spiritual prowess to the church and so he prayed for a miracle to occur and for her to live. I have not told my sisters about the pastor praying for a miracle, nor would in be wise to do so. It would not be a good witness for some of my sisters.
A few months later this pastor asked us to leave "his" church. He was very controlling and dominating. A little later he was asked to leave by the leadership elders because he was spiraling out of control. The "denominational body" replaced him with a new pastor with the same characteristics and it has continued nudging closure ever since.
The point I am making above, from my experience, is that God will heal people when it is in His will to do so, or he can withdraw and allow the circumstances to unfold to teach us a lesson about how we should pray.
The better prayer, I find in most circumstances, is to pray that God will include the person, we are praying for, among those whom He will draw to Himself and then leave the manner and miracles up to God to decide as to how He will achieve this prayer request. If God then prompts us to pray for a specific outcome to suit His purposes, then yes, we should follow that leading and pray accordingly at the appropriate time.
Physical healing is not always the appropriate outcome within God's will.
So often we rush into praying a prayer based on what we know from what we have been told and asked for by the person, without first establishing what God's will, within the circumstances that we find ourselves in, really is.
Shalom