Ehh, the only thing Axel shows us is that he's a basic pickup artist.
Pickup artist doesn't necessarily mean that you you can't manipulate. Manipulation also occurs using words and he can clearly use them damn well (Recall his first conversation with Ian and Cindy in Club how he interacts with Ian and Cindy). He just resorts to words to manipulate and if not than goes on intimidation, coercion etc. as we see his fight with Ian on Ivy's birthday.
Hardly a "master" of manipulation if he can't even prevent Ivy from getting pissed off with him.
I used the word "Beast" for him for a reason not "Master". He has all tools YET he has so little control over himself. This is what makes him suffer in long run.
He also flails helplessly while trying to get back Lena, makes an idiot out of himself in front of her multiple times, and potentially fails if the player will have none of it.
He plays guilt card with Lena, uses projection, tries to reflect that he changed etc all are just his words. That he does all the time but again it's his control that limits him. Whenever he loses his calm he is caught is a vulnerable position and Lena mentions this after Axel's fight with Ian after Ivy's Birthday party that he is same as always and won't change. That's the reason Axel fails trying to get Lena back. Lena knows him for a long time. Also note putting Ivy in a position so that she cannot tell anyone what kinda deal She has with him and She can't do shit to him cause it will back fire on her is also manipulation.
Axel and Ian both greatly rely on Persuasion but the self-control Axel lacks is what Ian has and the experience Ian lacks is what Axel has. Gaining control is difficult for Axel but gaining experience is not that difficult for Ian.
EDIT: I would recommend TWO Anime 1) Classroom of the Elite 2) DeathNote
You will understand what I'm trying to say. Both are short anime.
