I feel like the "Has Guts made the world a better place" discussion is kinda pointless.
Guts isn't out to make the world a better place. He's neither actively seeking to improve the lives of strangers while also not trying to make them worse. He's just trying to make his way through. And it's not a matter of him lacking empathy or anything like that, because he's long since reconnected to his human side and he never fully lost is ability to be a basically decent human being. If he sees someone suffering directly in front of him, yeah, he'll probably put an end to that. But he's not a super hero. For several reasons:
1. He can't do it. He's better now that he has a gang of friends that can watch his back, but that's for stuff like Farnise helping him gain access to restricted places with her connections and can take care of Casca in ways he can't and Serpico taking watch so he can get some sleep and Schierke keeps his sanity in check. He needs all these people just to help him remain semi-functional. If he can barely keep his own shit together, why would he even consider trying to take on the vastly bigger project of fixing the world?
2. It's basically not in his character. He's always been disinterested in the long term, larger plans that Griffith plotted when he was trying to rise to power in Midland's court. He has always been a fighter and never aspired to be much else beyond that. He was never even interested in being the Hawks leader, with him being kind of uncomfortable when the idea was presented when they realized Griffith was crippled. He could have lead the hawks, maybe, but he didn't want to. He's not political, he's not philosophical, he's barely social. Larger problems like the state of the world have always been beyond his need or interest. He's only ever fixed anything by killing it and while he certainly wants things to stop trying to kill him, I don't think he'd know what to do with himself if that ever actually happened and he didn't need to fight anyone anymore. Finding whatever he needs to fight next is basically all he really knows how to do.
3. Also character related, to 'save' the world, you generally have to hold some kind of affection for it, or atleast people connected to it. Superman saves people because the Kents taught him to always be considerate of others, Batman in TDK trilogy saves Gotham because his parents had a dream of saving Gotham. Guts' was born into a mercenary band who travels from place to place, joins another mercenary band that traveled from place to place, left it to travel from place to place, and now continues to travel from place to place. As far as I can tell, Guts never had a stable home of any kind.
In his travels, Gut's doesn't really make friends. Like, what, there's the deformed guy in the first few chapters. That little girl who he kinda protected (I wouldn't call what she is a friend even, just a kid and he didn't really want to see her hurt). Beyond that, I genuinely cannot think of anyone else he's created a positive or meaningful relationship except 1. the Hawks and 2. His current traveling party. And all these people are outcasts or without their own home as well. The hawks were specifically chosen for this (griffith wanted or atleast attracted people without other options and had to try and achieve their dreams through him), while his current traveling party consists of a former Iron See Knight and Noble whose effectively abandoned her position (and a brother whose abandoned it with her), an orphan who is without a home as well, and Schrieke whose lost her home in the attack we saw.
Guts is detached from the world and only makes connections with people who are similarly detached. Again, it's not to say that he or his team lack empathy or decency, but they, like Guts, are all just trying to make their way and not much else. It's outside of their scope. And unless I'm forgetting someone, the only people who actually sought to make an improvement on the world as a whole were villains (Mozgus, arguably the Godhand as a whole), whose true motivations are selfish. I think he literally doesn't even know a single person who'd go "We have to save the whole WORLD!" Why would he start then?
The only reason we're talking about this at all is because Griffith is using this as a selling point for why he's super awesome and everyone should just live under his rule. Except we know who Griffith...or more accurately, Femto....really is. Whatever his intentions are, they're unlikely to be something that actually betters humanity. So, trying to pigeonhole Guts with a "Well, how have YOU fixed the world" is just wierd when it's not something he's even trying to do and the person your comparing him to is probably going to commit genocide on his own city.