Don't get me started on that moment in Superman 2. That's my least favorite moment in any super hero movie, ever. I hated it as a kid in 1980, and I loathe it as an adult.
Yet, its existence alone contradicts Lois Lane's line in the crossover as something that's true of Superman—this Superman in particular whose history includes that moment. The other examples that I pointed out, most of which you didn't address, further contradict it as any true statement about Superman.
I would also completely disagree with you on the line that Lois said. It was a good way to describe the KC Superman's reaction to Crisis. He had obviously been traumatized and had lost hope, but he realized his duty to the Multiverse much in the same way that his traumatized comic counterpart realized that he needed to overcome his personal despair to battle the brutal heroes that had risen in the place of the JL. That's what a hero does.
It is a good way to describe KC Superman's reaction, but she didn't state it as just about him. She made a generalization—one that you then used to assess other versions as less worthy—and that is why the line, and your interpretation of it, don't work. Lois said, "Guy never quits no matter what Earth he's from, huh?" If she had left it as, wow this guy never quits, it'd make sense. But, as it is, the only reason he's with them is because he's the Paragon. It's not like they went around to other Earths recruiting any and all available heroes, including all Supermen. He's there because he was singled out. He's at a different stage in his life with his wife dead and his kid grown up (he'd be about 19), so he's more free to go on this adventure.
So, if Lois' comment is just about how KC Superman keeps going, then it's fine. But if it's read as her commenting about Supermen across Earths, and then used to criticize other Supermen by comparison, then it's not fine, especially when this very same KC Superman is
Superman II and
Superman Returns Superman combined—both of whom quit.
Admittedly, I wasn't a huge Smallville fan, so correct me if I'm wrong, but wasn't the main theme of the show about a young Kal struggling with his identity on his way to accepting his role as a hero in the final season? That's what I remember about it, especially when he realized that there were not only threats to humanity on Earth, but cosmic ones as well. And after all of that, the epilogue is a guy who decides to chop wood? That's hardly a fitting send-off.
Yes, that's what
Smallville focused on, and he did accept his role as a public hero. He had been acting as a hero since the Pilot, however, and had defeated almost all of his major villains before he was Superman. He put in an additional 8 years or so before deciding to focus on family for awhile. He didn't decide to just chop wood. He decided to be there for his wife and daughters during the earliest years of the girls' lives (they're only about a year old!) without having to deal with the crushing weight of having to choose to respond to his baby's cry or a cry for help from a person in need. He also spent those years forging friendships and inspiring others who could take over in times of crisis, if need be. In one of the show's final episodes, Lois' father, General Lane, even offered this advice to Clark:
Can I give you some advice, Clark? Going to war having to deal with the rush of battle and the struggle to save lives it made coming home and doing the simple things difficult. But, you know, it's funny. It's the simple things, like taking a walk or dancing with your wife tucking in the kids, that make us human. Now, don't get me wrong. I've loved serving our country. I even got to be a hero a couple times. But if I had to do it over again I'd spend more time with the family.
Clark's approach to his work/life balance is always evolving. He's not unlike human adults in that regard. As far as one can tell, this isn't a permanent thing. It's more like paternity leave. And, based on the way other Supermen have been portrayed, and the way the Arrowverse has heroes like Felicity, Vibe, and Black Lightning all taking time off to focus on their personal lives and families, it isn't something that clashes with the ethos of these shows or presents SV Clark in a more negative light by comparison.