The analogy to the magical fifth bowl of ice cream is legitimate, but it also is lacking. It would seem to me that pain and suffering can also be God's answer to prayer, such as in the case of disease visited upon God's followers.
I think, again from a believers POV, that a little more needs to be added to what you said. Perhaps this is excess or unneeded, but it makes me feel better to bring it up.
Pain and suffering, whether of a believer or non-believer, are just part of life. IMHO GOD has given us many ways of dealing and alleviating much of it. We learn more each day about desease, its treatment and prevention, and also more about how to alleviate less understood pains such as metal anguish, regrets and concerns.
But there is more as well. Often, the strengths a person develops when dealing with trials makes the person better. Courage, sacrifice, striving, ambition even cooperation, inspiration and innovation are often the direct results of such challenges.
Aslan is not a Tame Lion