I understand your point but this is not "bad writing" at all. This is how the character is suppose to be, just by looking how the game presents himself tell us that the protagonist is a overpowered badass (talking about the original DMC here), and he's intended to be cool and not humanly.
Then what's the point of him being half human if hes suppose to not be "humanly"? Old Dante was half human not to show that he LOOKS it, but that he can have feelings as a human.
And i don't think it can be called a "lazy habit of the japanese", look at characters like Wolwerine, Hulk, Superman, Apocalypse, Dark Phoenix and so on, they are overpowered too but they are cool, my personal favourite from the HQs is Wolwerine.
Don't forget Deadpool; the biggest non-death character.
At the same time we have characters like Solid Snake or Kenshin Himura (from Rurouni Kenshin/Samurai X) who is very human and much more realistic than these other i named. I agree with you in this point, but it's kinda limited too, Donte acts like a rebelious teenager like most people already was before, that's why people can make that "connection". But i prefer to see Dante acting in his funny way than "making a connection" with Donte.
And your entitled to that, but I prefer to laugh, cry, and actually feel like I'm going through the same issues with my video game character.
But after all, this is a trait of the half/quarter-breeds on DMC and if they would fight against Donte this has to be considered. But as i said twice: it's hard to compare because both designs were intended to different purposes and were made with very different standards.