The four things I notice and hate the most in Gai's (bad) characterization:
Intelligence: In some fics they make him completely stupid, with no ability to conform to social labels or understand what they say to him without rethinking it, and that makes my blood boil because this guy is anything but stupid; He is an avid learner and always seeks improvement (genin at 7, chuunin at 11. He may not be Kakashi but he is still quite a lot, right?), able to predict, if I remember correctly, up to a hundred movements of his enemy before to be executed, someone who thinks quickly in battle and very adaptable.
My God, he drives NUNCHAKUS and you think he's incapable of concentrating? I understand that it is one thing to sit down and study and another to train, but I don't think GAI, of all people, wouldn't take on such a challenge. Appearing empty-minded is his facade, his mask. The only way I can accept that he's pretty stupid is if it's because of the trauma of losing his father, he clings to the attitude of a child as a way to feel like he's back in his childhood. AND YET-
Darkness: This man was literally beaten by chuunin because when he was a child just for being the son of a outcast of Konoha, they made fun of him and probably isolated him from the rest as a child, and he has also been under a strict exercise regimen since he was 5 years old. An exercise that made him fall from fatigue and pain, and he, despite everything, continued to get up, continued to force himself to overcome the pain. Gai's darkness is not easily detected because he is not visibly cruel to anyone but himself; The only way he is easily seen is with his relationship with Lee, his dedication to put him through everything he put Lee through even though he is the person Gai loves the most (possibly after his father). The way he pushed his (Lee's) limits to the point of telling Lee that he should face death to hold onto some hope for a better future (to be a shinobi again) is very dark. The relationship he has with Rock Lee ironically brings out the worst parts of Gai, and there we enter the next point.
Cruelty: Gai is a character who has been shown to have an extremely strong code of values, in which benevolence always comes first; He is empathetic in a world where that is condemning, he is kind to people who at best only make fun of him for how he looks. In short, a great person. But that does not mean that he is not cruel, that he hesitates when killing; he is still a soldier, a child soldier who participated in a war based more on ego than anything else. His moral code does not prevent him from killing, but rather makes him limit himself, to limit himself to what is absolutely necessary. If he has defeated his opponents and thus achieved his mission, then he will not kill, because the rest are shinobi like him and also had a mission.
We've only seen traces of Gai's cruelty throughout Naruto, small flashes of what he truly is in battle. Do you seriously think that the title of Beast is achieved only by defeating enemies? It is not even a specific animal, but literally: Konoha's Beast of Prey.
And what is a beast but an animal that kills cruelly? One kick of his was capable of breaking rocks when he was just a child. What prevents him from punching through his opponent's chest? Breaking skulls using just his fingers? You're not going to tell me that someone like him, with his strength, is not capable of ripping off your arm in a single movement.
Gai is capable of great, great cruelty cultivated by years of being humiliated by the village he now protects with his life, by the Village for which he destroys his body day by day. Still, his morals prevail, but it does not mean that cruelty is inappropriate for him.
And possibly the root of all his problems...
Death Wish: Dying for the Village is something that is as ingrained in how Gai thinks as any Konoha child, but this takes a drastic turn when his father sacrifices himself to save him. His father was, despite being ashamed of him, his World. The only person who loved him with everything, who showed him sweetness and tenderness in everything, he who took care of him as the most precious thing he had. In a place where everyone hated him and slowly began to change because Gai was useful to them, only his father loved him unconditionally, no matter what.
It is not specified how old Gai was when his father dies, but he can be placed after 11 and before 14, and that is possibly the source of what he is like; totally adhered to what his father was in an attempt to demonstrate that Maito Dai was a great man and shinobi through his legacy of the Eight Gates, his greatest and only technique. It is known that before he was 20 he had already acquired his title of the Blue Beast of Konoha, so it is accurate to say that he already knew how to open the Seventh Gate, at LESS THAN TWENTY YEARS OLD, the time it took his father to master the technique.
Gai's desire for death and his perspective of it is shown by his speech about Lee's highly risky surgery; If he can't live fully as a ninja, then he doesn't want to live. For him, Death is a price, the most precious coin that he is able to throw to prove something, to prove that he is worth something in a world where Death is common, where he was expected not to survive, much less prosper.
He lives life to the fullest, being his best person, enduring whatever it takes because he knows that his end, his death, when it happens, will show everyone that he was never weak, that he was incredibly powerful, and for someone who grew up being treated as the lowest scum except by his father, who ended up dying in a blaze of glory as an outcast, a death like that is the highest he can aspire to. For him, the only destiny is death, and the only way to prove his worth. And that's not fucked?
(And if you want to add another tragedy, possibly the Eighth Gate was a relief during the war because Gai's death cannot go unnoticed, hidden. Being someone who had so many limitations, being at a significant disadvantage, and being sent to war so young, where the majority are children or other young people who die anonymously, the Eight Gates were his way of establishing that no, he would not be killed, because he would kill himself first. Oh, now i know why he respected Kisame so much at the end.)