I think quite a lot of action movie heroes fit the Designated Hero bill (I'm not talking about ones where the hero is clearly supposed to be an anti-hero nor ones where the hero is supposed to have some kind of mental health issue, ala the Rambo movies even though Rambo doesn't kill anyone in the 1st movie).
So many of them are borderline psychopathic, completely unaffected by the acts of mass slaughter they commit against hordes of hired security goons who are just doing their job to perhaps, for all we know, to support a family (in some cases said goons might not even really know what the bad guy is even up to and they're just trying to stop this homicidal maniac who's burst into the building and started shooting and stabbing everyone in sight). Sometimes the security people even look like they work for a security firm rather than the bad guy persoanlly. Yeah, the hero might not have much choice but to carve his way through these people to get to the bad guy, but some acknowledgment on the part of hero of the bloodbath he's created would be nice to see. And if you make a smart ass quip when you (sometimes accidentally) kill someone in a horrific manner, yeah you're kind of fucked up (btw I know Bond was orginally supposed to be a a bit of a psychopathe but plenty of other action heroes do the same).
One example that's always bothered me is in Die Hard 3 when McClane shoots a goon who says something to him in German a split second before he gets shot and McClane says, "What was that?" in a sarky tone. One of the secondary bad guys appears out of no where, hits McClane and says, "He said don't shoot." and Mclane doesn't react in any way to that, ever. Not even a slight hint of "Oh fuck, oops." Nothing. I know Mclane is meant to be a bit of an asshole, but fucking hell. He's just semi-accidentally kiled a guy who had surrendered and he straight up doesn't give a fuck.
Another designated hero is Captain Archer in Enterprise. He commits several, unecessary acts of genocide and mass murder which, if the show addresses the morality at all, get justified with a hand-waving single line of dialogue that rarely, if ever, actually justifies anything. There's even one episode where he chucks someone in an airlock and threatens to open it if he doesn't tell him what he wants to know - after the scene is over it's never mentioned again, like it didn't happen. For contrast, as far as I remember Piccard was able to get through all kinds of situations without psycologically torturing or threatening to murder anyone. I don't think even Kirk didn anything comparable. Archer also seems to be constantly angry/annoyed and shouting at people, and if he's not shouting he's being sarky and condescending. He's also bored by astrological phenomena and kind of a racist. I know it's meant to be the early days of Earth-Alien relations so it makes sense a lot of the characters are a little bit racist towards aliens, but not the fucking Captain. He should be leading by example and he should be the person the viewer wishes he was. Call me mad but I don't aspire to be an angry, sarcastic, murdering racist.