I always kind of laugh at this new-found notion of white characters being 'generic'. Like, moving a character's skin slider would automatically make them interesting.
For example, Ezio, white but charismatic and interesting. Connor, Native American but bland as fuck. Characters are interesting based on how well they are written, not their skin colour lol.
Even after reading OP's examples I'm having a hard time distinguishing "a good character who happens to be white" from "a good white male character." None of these characters are "about" whiteness, so I'm not really seeing how this question can't be reduced to "good characters in games (most of which are white because that is the current default)."
Could OP perhaps lay out the criteria more clearly for what is "white done right"? Is it a white character who sort of needs to be white because of the cultural context of the game like BJ? Is Michael from GTA evincing a uniquely white upper-class malaise?
I think there's an interesting discussion here (that will be completely derailed, naturally) but I'm not clear what it is yet.
There's not a fine line between "good white" and "white good." I would say as a whole, someone like Marcus Fenix or whoever's headlining the next Call of Duty title are bad examples because you
could change their race and no difference would be made. Now that I'm starting to see some examples, I think examples of "white characters who are good, but contextually justify themselves" can fall into two major categories:
A character is wholesome or good, and being (or not being) a white male would subject them to different societal repercussions. BJ Blazkowicz has an emotional crutch in that his family is Jewish and is being directly targeted by Nazis. John Marston, on the flip side, is white in an era where not being white is a dangerous game. However, Marston is progressive and is overall still a good character from the viewer's perspective. A bad example would be Doomguy or Duke Nukem, because they could be virtually anyone going through a testosterone-poisoned power fantasy and it wouldn't change the game.
A character has unique or otherwise breakout design, from looks to personality, and defies their expected genericism. They are, in some way, flawed. Michael De Santa, while old, white and gun-toting is still interesting because he has downsides and from a legal perspective is still a piece of shit. Likewise, Max Payne is more of a subversion because while he's kinda samey on the outside, he's battling plenty of demons from taking so many people out and his age is catching up with him. Even Professor Layton works thanks to the setting - he's a stereotypical English gentleman and looks (and acts) as such, and him being Pacific Islander or Native American, for example, would be dissonant. A bad example would be Aiden Pearce, because while he's still admist a conflict as the plot demands, he's still falling victim to not really pushing the envelope from a design or narrative perspective and is pretty one-dimensional. I'd say the blurred line or halfway point (between good and bad) for this second option would be Kratos, because while he's Greek and perpetually ash-coated, as well as the epitome of dudebro, he does have
some humanity - at least back in Ascension's day and age.