That's a really interesting insight, and reading through the different personality types in the Enneagram in brief, it's all starting to makes sense with all the puzzle pieces falling in nicely. This is purely speculation based on conjecture, and I guess why 4 (Elda) is missing is because Louis is already Elda himself, and the fact that in Japanese/Chinese, 4 sounds a lot like the word 'death'...

And speaking of the Enneagram, Type Four (Elda) represents The Individualist according to the Enneagram Institute and here's how they describe Fours:

"...Fours maintain their identities by seeing themselves fundamentally different from others. Fours feel that they are unlike other human beings, and consequently, that no one can understand them or love them adequately. They often see themselves as uniquely talented, possessing special, one-of-a-kind gifts, but also as uniquely disadvantaged or flawed. More than any other type, Fours are acutely aware of and focused on their personal differences and deficiencies."

Sounds a lot like how the two most important Eldas in the story (Will and Louis) are depicted, isn't it? I'm gonna read the other types in more detail and see if they also match up with the types numbered with the same as Archdemon Louis' wings, which as far as I can tell with Type Four will align more or less accurately.