Ok... This might be a long one...
Starting off, the hair. Yeah, the color mattered, let's not even pretend it didn't, it was a tremendously defining characteristic of the character so let's not pretend it wasn't a big deal; However, it's not the hair color that bothers me, it's the style. It's so pop. There are people in boy bands that have similar cuts. It reminds me, constantly, of who the target audience is. It's the kind of hairstyle you'd find opening any random magazine currently on stands. Yeah, the same could be said of the last 2 games but for a game that is supposed to be about been rebellious and fighting 'the man' finding the protagonist sporting a hair cut right off a teen magazine seems rather hypocritical.
He character is inconsistent. He is rather erratic, he's an a'hole one minute and considerate the next. Granted, his character is the victim of bad writing but it's still there. He is what ever the scene call for him to be and not what a flushed out character should be in the situations he's put in. He doesn't really grow at all, and if he was never meant to then that would fine, but as this is supposed to be a character arc then it's an issue. Add to that he way he talks. Yeah, the cursing, too, but I mean his actual speech. The way he says things sometimes is bland (and sometimes is slurred). There aren't that many ups and downs in the way he talks and the things he says so it comes off as making the game seem like it took no risks with his character, which is kinda what I mean. In the diverse world of video games he doesn't really stick out much, there are plenty of characters around like this one.
He's not clever. He drops the dumbest one liners and he should be called on them.
He's not that interesting looking. Yeah, I'm sure he's handsome, who isn't in video games, but he isn't interesting to look at. He looks bland, generic and he wouldn't really stick out in a crowd. I know that people love to point out that as a positive but it's not. This is a video game not witness protection. His design should give him a personality on it's own and here it just makes him bland and generic, there is nothing unique about him. Even his color scheme is bland and boring. And I know how much people love to drop the 'he is the kind of character you see walking down the street' line but I wouldn't and don't want to play as some random dude I see walking down the street, I want to play interesting characters (Which Nathan Drake qualifies as in the same way Indiana Jones qualifies; they have personality and are put in interesting situations), specially in my fantasy or action games. The game is not realistic enough to warrant realistic properties, specially from the protagonist of a game that is this unrealistic.
Before anyone decides to drop the 'so the previous DMC game were better at this or that, then?' I'll add my next point. This was supposed to be better than the previous games by leaps and bounds in every department. This game was advertise as been as good as literature and film and bring a sophistication to the franchise that only NT could deliver (and I could make a joke on NT's expense about that but won't). This did nothing of the sort and we all know it. This game is no better than the rest of the franchise in so many places, worse in others, but it didn't do anything for Dante. He is not the next Hamlet, nor has he been elevated from what the other games had to offer to a more profound or fascinating character, which was the point of the reboot in the first place and if it didn't even do that... Well, then.
He really is a fan fiction version of old Dante. There is so much here of what seems like someone's idea of what Dante should be like rather than a genuine interpretation of a younger version of him with anger issues. This comes off as a teenager's power fantasy about how his characters does a'hole things and gets away with it. I read a few of these when I was in high school, he really comes off as that kind of character.