Hell no "Edgy" Ayanokoji is fun to observe
Not when that's the only thing that's going for him. In the same way you get bored by overpowered MCs in e.g isekais it gets saturated when he's only cold, only playing mind-games and only focusing on himself in the anime.
Not everything has to be exactly like the light novel a few differences make it fun
This time it has to, otherwise it'll suffer the same fate as Fate Unlimited Blade Works did where Shirou's soliloquies where terribly undermined, lackluster and (crucially) essential to the story but nowhere present in the anime adaption. Ayanokouji's monologues are the core of CotE, and not utilizing the whole picture of his thoughts and ideas in turn undermines the anime's presentation in my honest opinion. It doesn't have to be word for word, chapter for chapter accurate, but the wiggle room is tight. Books adapted that way doesn't translate well over to a filmed medium, but the anime does have monologues and they worked in season 1 so just represent them more accurately instead of pleasing depressed emos.
Hes plenty complicated in the anime and in the light novel he has plenty of mind games
Disagree. Anime Ayanokouji could be dissected down to "I'm smart, have a mystery past and emotions are just a tool for me to utilize" while the light novel depicted a different reality. One in which he's affected by the new environment, new people and most importantly it makes him question earlier notions of his deep-rooted idealistic views. The anime makes it seem like he's solved the human psyche and could never be wrong. A character without flaws is set up for failure, that's why isekais are (were perhaps) hated, but light novel Ayanokouji was flawed. Horikita is just a more "visible" version of Ayanokouji in the end of the day, if that makes it easier for you to understand.
Its overexaggerated how different he is from the light novel or that hes less of an ambiguous character.
Over exaggerated ≠ wrong.
In the Ln he shows a smidge more of emotion but compare it to a normal person and his facial expression is pretty cold
That's what makes the light novel moment better, letting his emotions slip through his ideological facade because he's genuinely angry with [those who know who, knows] for what he did. That would just appear so out of character for him if all he's ever been is cold, edgy and rational. He would never had gone to such lengths otherwise.
He also has never been shown to make a real or even fake smile in the ln
True, but I didn't advocate for him to literally show emotions in form of expressions. I wanted the viewer to get to experience his soliloquies to understand that he ain't that edgy as he appears to be.
Season 1 aside from having things out of order and erasing kei
Season 1 didn't only erase Kei, if I understand what you mean by that. They just threw her in there like she and Ayanokouji had been establishing a relationship already when that pool sequence happened after they'd even started to talk with each other.
It's flawed, exaggeration or not. They're handling such a meticulous piece of literature that if the director didn't happen to be the author himself then changing anything to the characters or story would be a mission set out for failure. It's a light novel that deserves to be adapted well, because it's quite frankly a one-of-a-kind.