Thanks for a great read.
The debts to Moorcock always felt explicit (stronger than Zelazny) when I started playing Basic in the lat 70s, and I think the cool-factor is a big part of its success. Elric as a servant of Arioch, lord of Chaos was rock'n'roll, and the fact that he was a wasted king of a wasted people who rode dragons, but only when they could wake them up resonated well with adolescent minds.
But there were disconnects.
Elric himself wasn't chaotic in his behaviour. Yes, he served the lords of chaos and had a patron and summoned them and cast their spells, but his reasons for doing so always felt that it was due to something arbitrary: both something that had been determined long past that his ancestors served these gods, and that the granting of occasional boons reinforced the association.
That is to say, Elric was chaotic because (a) the people of Melinboné tended towards chaos [i.e. they had a natural alignment, the same way (all) monsters do], and (b) Arioch gave him his cleric spells. Elric's association with chaos (as I saw it, and I think this remains true) was not about his behaviour, but that he was a pawn in some cosmic game that was separate from any choice he made. Sure, he had a soul-sucking life-giving sword and that reinforced that association, but I don't think that there was ever really presented an alternative for him, so any element of choice there too was diminished. And because he was a good pawn (or arguably bishop or knight), he continued to receive benefits from Chaos.
Shifting that association onto D&D was straightforward: some creatures had natural alignments (even blink dogs, which by AD&D were also intelligent enough that it mattered), and aligned forces could give powers to notable adventurers.
And with the rules for Paladins at the time, it was even possible to lose your powers if your actions differed too much from the beings that were empowering you.
But the cool factor, for me, was important: chaos was cool because of its anti-hero in Elric, and there were no problems with characters of multiple alignments hanging out (doesn't Moonglum disparage Elric's association with Chaos?). But the expectations of behaviour were only really present if you wanted to be a paladin.
Fast forward twenty years or so, and alignment has been watered down: chaos and law aren't forces in eternal cosmic conflict, but reflected whether you would steal bread to feed a hungry person or not. It became an anodyne choice reflecting personal morality, and not whether you were caught up in a cosmic struggle. But the cool factor associated with Chaos (and 20 20+ years of gaming) still had a strong pull: many players would say their characters were CG becuase elves and freedom and stuff, but it was tied to something inside the character, personal agency, and not being caught up in a centuries-old conflict of unknowable beings toying with mortals.
By making it about personal choice the paladin-factor made better sense (players could control their characters), but exactly parallel to that development was the sense that it shouldn't work that way: that characters should be able to be CG paladins or they should not be stripped of their powers by an arbitrary god or DM, even as the assoication of alignment with personal choices became stronger.
It was never consistent: alignment reflected natural dispositions, a source of supernatural abilities, a compass of personal ethics, and an element of cool. And, no doubt, each player weighed those differently depending on their table and personal preferences. And even if the source was Moorcock, by the time it hit a game engine it necessarily became something different.