Does God magically intervene in the world?

If God *does* magically intervene, then I find a theological problem arises when some prayers go unanswered.

For example, consider the case of someone praying for healing that doesn't eventuate. As I believe in a God of unconditional love, I don't think God would ignore prayers, choose those to be answered on a whim, or punish people by refusing to answer prayers because of a lack of faith or
insufficient piety.

Perhaps, God could intervene but chooses not to, for reasons such as the personal growth of the individual who is sick or a greater good that arises from their illness? I do believe good things can arise from bad situations. A period of illness can motivate us to re-focus on what is really important in life. The death of a love one could motivate someone to dedicate their life to medicine - treating and curing many hundreds of others. However, I am uncomfortable with the idea of a manipulative God who is content to let one person suffer for the benefit of others. It doesn't sit well with the shepherd who leaves the 99 to rescue the 1. Furthermore, if God is all-powerful, then presumably God could devise a way for the greater good to be achieved and the individual to be healed.

This leaves me with the belief that God does answer prayer, but that prayer doesn't work through magical intervention. I believe prayer changes us, leading to our own action to bring about the change we are praying for. I am also open to a natural, biological mechanism in the universe, which sits grounded in God, that we don't understand yet but that we unconsciously tap into when we pray.

However it works, I believe in the value of prayer

In regard to the interventionist notions of prayer in the New Testament: more people at that time would have believed this to be the way prayer worked than they do now, including the authors of the biblical text. Thus, for example, the stories of the miracles of Jesus, are either a record of actual events where the healing was interpreted to be (but wasn't) magical/miraculous, or stories written to help convey the theology people were building up around the person of Jesus (but not actual events).