However, if one is of the opinion that God does not always intervene to make sure that good things happen to good people, then it's not much of a stretch to also believe that he's not taking an active role in all the bad things that happen.
It's a question of whether God directly intervenes in everything that happens, or whether he allows events to occur naturally.
I hold the latter opinion, and believe that prayer is the asking for active intervention which might otherwise be withheld.
I agree. IMHO, the meaning of the Garden of Eden story and God's covenant with Noah is that human beings have been given the gift of free will and conciousness and God will not again destroy mankind even if we use our free will for evil. The evil in this world comes from the actions of people, not God.
I don't know what you mean by "intervenes." I think of divine intervention as the miraculous. Normally, God allows things to occur "naturally" in the sense that he sustains everything in existence and also sustains human free will. He also works supernaturally as he bestows grace upon us.
I hold the latter opinion, and believe that prayer is the asking for active intervention which might otherwise be withheld.
Since God moves us to prayer, I don't think it's quite correct to say that God's "intervention might otherwise be witheld."
In hearing our prayer God does not change His will or action in our regard, but simply puts into effect what He had eternally decreed in view of our prayer. This He may do directly without the intervention of any secondary cause as when He imparts to us some supernatural gift, such as actual grace, or indirectly, when He bestows some natural gift. In this latter case He directs by His Providence the natural causes which contribute to the effect desired, whether they be moral or free agents, such as men; or some moral and others not, but physical and not free; or, again, when none of them is free. Finally, by miraculous intervention, and without employing any of these causes, He can produce the effect prayed for.