“A hasty explanation can suppose that to pray is a futile act because a person’s prayer does not, of course, change the changeless; but in the long run would this be desirable, could not the changing person easily come to repent that he had managed to get God changed! Thus the true explanation is also the one and only to be desired: the prayer does not change God, but it changes the one who prays.”
—Søren Kierkegaard, Edifying Discourses in Diverse Spirits
While some prayers may be petitions and some petitions may be prayers, it does not follow that all prayers are petitions. But seeing as @seawulf575 has already demonstrated this more than adequately with his examples, I’ll just say that I disagree with your interpretation of “The Soft Parade.” It does not imply that petitioning the Lord is the same as praying. It implies that petitioning the Lord is not something that prayer can actually achieve.