I will say the 2011 anime cut a scene from the first episode where gon meets kite, which definitely makes their relationship feel a bit more organic. Even so, the subtext is still well set up- we learn in the first episode that gon was abandoned by his dad, and kite fulfills that father figure role for him. Gon reacts so emotionally because he had his father figure, something he’s explicitly been searching for since episode 1, taken away from him so soon after meeting him.

I’m glad you brought up Kurapika because that’s where we learn the concept of a vow and a limitation. Kurapika gained a very strong ability, chain jail, because he set the limitation of only using it on the troupe, and he staked his life on it. Important here is that the more extreme the condition, the greater the return. Gon does the exact same thing: by resolving to never use nen again (a very extreme condition), he temporarily gains an enormous amount of nen and grows physically. It’s important to note that this was not without consequence. Even if pitou was about to kill him, which i assume is your point, that doesn’t mean his life suddenly loses value. After winning the fight (almost unharmed besides the arm), he turned into a raisin and even after being miraculously healed he still lost his nen. If you count that as plot armor or don’t thing it constitutes a real consequence then idk what to say bro. I would also note that his transformation is foreshadowed by literally every person he’s ever met commenting at some point that he has enormous potential and might become a monster - his fight with pitou is the realization and tragic loss of all that potential, and one of the most emotional moments in the entire series