The way I look at it is this-- if we don't EXPECT or BELIEVE that people will really be healed when we pray with them, even miraculously so, then I don't think we will have very good results. Of course we know that everyone does not get healed, but that is not God's fault.
We all die, and most of us will die of disease. So how is it not "God's fault"? Unless you mean its Adam's fault? This statement implies that were it not for weak faith (the persons praying for the sick or the sick persons?) we would be healed. But even if we are, it is only temporary.
The church we attended for many years had a long time member who got cancer. His outlook was not good. He was anointed with oil and prayed for more than once and was sure he would be healed, but he gradually worsened and died. Another man, not long a Christian, was diagnosed with colon cancer. He was in despair and contemplating suicide. The church was praying for him and the surgeon went in and found no cancer, only a small scar. So are we to believe the man with much faith died because some (or all) who prayed for him had little faith? And the man with little faith was healed when the same people prayed for him?
IMO we should pray for the sick, in hope, and realize God will answer in His way.
Last December our dear niece died at 51, after suffering for a long time. She was a good Christian person we loved much. The surgeon had advised her that "it was time to roll the dice", i.e. risk surgery for a chance to regain her health. We all prayed for her and I believed she would get well, but complications set in after surgery and she died. I just looked again at the card I received from her sister who loved her so much. She closed with: "Our hearts are broken. But God answered His way."