Okay... there are some spoilers ahead.
For one thing, yes, that is a view Moorcock often takes where "gods" are concerned -- that they are much on the level of spoilt children a lot of the time, often quite vicious and brutal, and certainly the majority tend to be more concerned with asserting power and dominance than with any sort of benevolent (or just, for that matter) approach toward the beings who pay them obeisance. And both Elric and Corum slay their share of gods -- Corum destroys both the Sword Rulers and the more distorted, primitive gods of the Fhoi Moire, who have long outlived their usefulness yet cannot die naturally and fear death -- when, in fact, if they had gone when the time came, they would have been remembered with some honor and kindly sentiment as opposed to being viewed as monstrous, cruel, and bloodthirsty; while Elric slays both small gods and even threatens the Lords of Chaos -- and defies the Lords of Law at various points (the most important being in his conversation with Lord Donblas, the Justice Maker, where he forces even this austere being to acknowledge the essential truth of what he's saying).
As far as Elric (or Corum, for that matter, though to a lesser degree) -- part of the point with him is that he, like so many of Moorcock's "heroes" in his fantasies, is prone to give in to circumstances too often; either that, or to that more primitive, Melnibonéan tendency toward particularly malicious and cruel revenge. And each time he does, it costs him a little more, until finally he becomes entrapped in the role he originally fought so hard against. Yes, he suffers setbacks, but whenever he fights against that tendency, and tries to assert himself, he usually does make some changes... he alters the web of Fate, as it were. Corum is less vengeance-driven, but also tends to play out the role assigned to him rather than asserting his individuality; yet he does make strides....
And, don't forget, both these series are actually part of a much larger tale, where these themes are played out not only in more detail, but in a way that allows much more complex examinations of the ideas Moorcock is addressing. Elric's time, for instance, is called a "prelude" at one point, before the real play begins -- it serves as a more elaborate example of the theme Moorcock addresses from a different angle in The Rituals of Infinity. And, even in his failure and death, Elric manages to bring a little more justice, a little more sanity, and a little more rationality and kindness to the world -- albeit it will be the world that follows his, not his own.
Which, essentially, is the theme of the Eternal Champion cycle (and, to be honest, all of Moorcock's fictional work): the Eternal Struggle to achieve that balance between the individual and society, order and chaos, freedom and responsibility, cynicism and hope, romanticism and the realization of the richness of the "mundane" lives we lead, tradition and change, etc., and the dynamic tension and variety this never-ending struggle gives to life. As Moorcock notes, the steps we take toward true justice and an enlightened society are incremental, but each one is, in its own way, a small triumph.
Some of his books, of course, address the hopeful side of this more directly: The Blood Red Game, The Rituals of Infinity, The War Hound and the World's Pain, Mother London, Blood, most of the stories in The Time Dweller and Moorcock's Book of Martyrs, the Dancers at the End of Time books, The Dragon in the Sword, and so on. But practically all of his books address this idea in the text at various points, and certainly by implication. As I noted, this is the major theme of Moorcock's entire oeuvre, and the vision that (to me, at any rate) lends it its special place.
Incidentally, it is this I mean when I say that Ellison's "I Have No Mouth and I Must Scream" is, in the end, a more positive story than is often realized. After all, even with what Ted is going to have to endure for eternity, they won. They defeated the God AM, by recovering their humanity; and part of the reason (it seems to me) that AM has done what he's done to Ted is to attempt to rob him of that humanity... but even so, Ted has the knowledge that they won, and so -- and again, for eternity -- has AM.