I agree with everything you say in this post.
I've never seen a product or had a play experience in which the use of alignment generated a fiction that broadly conformed to the Elric stories. Perhaps B2 KotB comes closest, but the Lords of Law and Chaos don't seem to me to be implicated in B2.
B2 is probably closer to Anderson's Three Hearts and Three Lions than Moorcock's Eternal Champion series. In both B2 and 3H&3L the Law/Chaos divide is racial and geographic. In both, Chaos surrounds the realm of Law and constantly threatens it. Both worlds are bipolar, with Law being good and Chaos evil. One difference is that Andersonian Chaos represents a more fundamental threat to the natural order -- it seeks to bring the whole Earth under a perpetual twilight.
Moorcock's universe is tripolar -- both Law and Chaos are undesirable if taken too far. On the most obvious reading, the Balance is the only true good. However Moorcock can also be read as rejecting all banners, ideologies, and gods, even the Balance. The Law/Chaos divide isn't strongly racial though the Melnibonéans, Elric's race, are allied with Chaos. Both sides are in constant conflict throughout the Multiverse, without any clear frontier or a sense that any place belongs to one side in perpetuity. Law or Chaos conquer entire planes and the opposition takes them back. An exception is the city of Tanelorn, which is of the Balance.
B2 The Keep on the Borderlands (1980) Gary Gygax:
The Realm of mankind is narrow and constricted. Always the forces of Chaos press upon its borders, seeking to enslave its populace, rape its riches, and steal its treasures. If it were not for a stout few, many in the Realm would indeed fall prey to the evil which surrounds them.
Three Hearts and Three Lions (1953) Poul Anderson:
Holger got the impression that there was a perpetual struggle between primeval forces of Law and Chaos. Humans, except for occasional witches and such-like, were, consciously or unconsciously, on the side of Law; the Middle World, which seemed to include such realms as Faerie, Trollheim, and the Giants, was with Chaos — was, indeed, a creation thereof. Wars among men, like that now being waged between the Saracens and the Holy Empire, were due to Chaos; under Law, all men would live in peace and order, but this was so alien to the Middle Worlders that they were forever working and scheming to prevent it and to extend their own shadowy dominion.
If Chaos wins, it may be yon twilight will be laid on all the world, and no more o' bricht sunshine and green leaves and flowers
The world of Law, of man, is hemmed in with strangeness, it is like an island in the ocean of the Middle World. North of us live the giants, south of us fire-demons. Here we are close to the eastern edge of the world, and know well of such places as Faerie and Trollheim.
The mighty rolling of hoofs, uncounted hoofs raging over the world, the sound of shrieking and of blown horns, the death-like rattle of arms. "It is the hosts of Chaos," he said. "All of them, riding forth to whelm the world of man."