The answer of your ranting is in your rant itself. There's children, children, happy and excited children are full of energy, they won't stay still before their object of affection. A happy kid is better than an isolated and sad kid, which is shown between Arylen and Persion the whole manhua until now. And to be honest, kids aren't the only one who run around or behave like he does, I saw grow up male lead acting like that each time they heard the ml was around or in danger, hell even Persion father, Edward, would act like that if Azani was before him or he wanted to see her. And yes he's a crown prince thus, for his kingdom he's the world that others bow to and revolves around him.
Even if we see the attendants crying because of the misbehaving, I don't think other ml, I'm some manhua, are better in manner towards their employee...
Ok does someone actually ever scood the prince. Like I know they are royals but him running around, doing whatever, no listening anyone is getting on my nerves. I know kids are entitled and little shits but like can someone actually tell him that the world does not revolve around him. I swear to good if he is the same bulldozer as an adult using the tactic of "if I just annoy her she will love me." I will drop this in heartbeat which sucks bc I love the FL a lot, her story is interesting.