An appeal to the heavens for divine intervention is nothing to take lightly, but every one I've ever witnessed seemed to be (in the grand scheme of things) a fairly straightforward, self-centered request. "Please don't let this be a tumor" or "please bring my child back" as opposed to "please cure cancer" or "please raise all of the righteous the dead"...and that's being charitable; most of the appeals I've heard personally revolved around not getting caught.
It occurs to me that even tossing about words like omnipotent, omniscient, and omnipresent, certainly a divine authority has priorities. Are we really doing the right thing by asking the being responsible for the movement of the spheres to help us hit lotto, or is that perhaps a distraction from more important matters? The Catholics have a system of intermediaries, but are very plain that your miracle is filtered up through to the Big Guy himself; he isn't delegating so much as he's hiring contractors to implement his designs. He still makes 100% of the decisions, which is perhaps why there are still pedophiles in the church and communists walking the Earth although a significant number of people have prayed for an end to both. It isn't that he's not listening, he just has a lot of shit on his plate. That, and he's ineffable / unfathomable, which makes the whole process damned infuriating because one never knows if something inconvenient is a part of the plan or just something that was de-scoped due to bandwidth problems.
What the world needs are second-stringers; someone who isn't saddled with quite so much. A specialist, if you will. You don't have the architect hauling concrete for the build site, and you don't ask the heart surgeon to put antisceptic and a bandage on a scrape, so why does humanity have the balls to ask the A-List of the divine world to get them out of parking tickets or help you pull a Jedi Mind Trick on the nice police officer and his dog?
For personal matters court then the intercession of unpopular gods, which being burdened with less may attend to you more.