Before we answer the question, I believe that we must make an important statement. God is a healer. His heart is that we be whole in spirit, soul, and body. All of these parts of us, working together, are what bring us to completeness. Our completeness cannot be done outside of the Holy Spirit and the sanctification process. It is a process that will continue for the length of time that we walk on this earth.
I believe the reason that God heals is very simple. We are broken and need healing! He is merciful, full of grace and love, which means that His heart is that we would be well. As believers we have been redeemed, but this continues to be a fallen world, and this, for now, is where we live.
Jesus was often asked why a person was afflicted, suffering, or blind, and His answers seemed to often perplex the listener. It was like the response that He gave somehow was not enough. God brings healing for His glory, and I will add, for our good.
When you or someone you know has been the recipient of outward healing, then you will understand this answer. The individual received healing from the Healer, not because he or she did anything that warranted a healing, but because God did for them what He does repeatedly. God did what was true to His character, a character that does not show favoritism, but which shows love.
Matthew 4:24 CSB Then the news about Him spread throughout Syria. So they brought to Him all those who were afflicted, those suffering from various diseases and intense pains, the demon-possessed, the epileptics, and the paralytics. And He healed them.