In a life without suffering, where you have only happiness, one would have a life devoid of some meaning. Some sort of 'emptiness' would preside. Without something to contrast against, the happiness loses its luster, and becomes the norm. Now there is no happiness and no suffering.
In a life of pure suffering, where there is no concept of happiness, the same principle applies. Without happiness to contrast the suffering to, suffering becomes the norm, the reality of life, and once again you have neither.
The greater the suffering it seems, the less it takes to please. From suffering comes much emotion, and much artistism. If Edgar Allen Poe had not suffered in his childhood, he would have had nothing to inspire his poetry. It is the taste of the forbidden fruit (happiness in this case) but the general lack of it, that creates a hole in the human heart. This hole is filled with emotion, with art, and with thought, much of which appeals to said lack of happiness.
Perhaps suffering is not "good", but good for us. Perhaps suffering is something people should learn to accept, and to expect, and in the long run, maybe even cherish, as means of expanding the soul.