That's a possible interpretation but a more common understanding is that it's an allegory of recent (at the time) Russian history where the old aristocrats were

That's a possible interpretation but a more common understanding is that it's an allegory of recent (at the time) Russian history where the old aristocrats were overthrown to be replaced by communists with lofty ideals, however those ideals quickly fell away and the society went back to something similar to what came before, just with a different set of assholes in charge. I think if you read more of Orwell's writing besides just Animal Farm, you'd see that he didn't think this was the only possibility. He was a democratic socialist and humanist. If he was saying it's the natural order of things under monarchy and under communism, that doesn't mean he was claiming it to be the natural order of things under all possible political systems. His political views had a wider scope than just this one short story.