(This is a more "big picture" consideration. But it relates to your point.)
IMO… What makes Superman philosophically interesting (and morally superior?) is that he has the physical means to literally rule the world - but does not. I.e., he’s the one exception to the concept of “absolute power corrupts absolutely.” But, realistically speaking, there should be a good portion of the general public who thinks there are no exceptions to this adage, and that society can’t and shouldn’t exist under this shadow. After all, even a benign dictatorship is still a dictatorship.
I speculate that the early comic book writers were aware of the ethically problematic nature of their own creation. So to rehabilitate and clarify, certain details were added to the mythos. Thus, for example, Superman was “deputized” by various police agencies. Therefore, he was not a vigilante (by definition), and was not (technically) acting outside the law. Likewise, the UN granted Superman special “international citizenship.” Therefore, he couldn’t be guilty of violating boundaries or sovereign airspace when performing his world-spanning super saves. IOW, Superman was “democratized.” By acting as an agent of established governments and legal authority, he was part of the system; he wasn’t a power above the system.
And, at a more practical level, Superman (himself) seems to recognize that he doesn’t deserve unconditional trust or faith. And to that end, he bestows (in some iterations) a shard of kryptonite to Batman (just in case). Alternatively, he indulges the military’s contingency of storing quantities of kryptonite weaponry (just in case). The latter has been represented in the CW’s Supergirl and (now) Superman & Lois.
To my tastes, these conventions are a tad too goody-goody, too anodyne, too Comics Code Authority. And collectively, they tend to dilute Superman stories of the moral complexity and conundrums I mentioned in the first paragraph.
That said, I (of course) appreciate that more wholesome, “family friendly” versions of Superman are likely to minimize the tricky philosophical implications of the mythos. Moreover, the narratives are often constructed so as to fully justify the “kryptonite contingency” trope. I.e., occasionally, Supes actually does go rogue. Or Kryptonian villains show up. Etc. So one way or another, squirrelling away kryptonite proves wise.
Yeah, I believe that Superman's "moral superiority" or more accurately, the idea of it, is generally attributed to one or both of two factors: his human upbringing w/ the Kents and/or his alien heritage. With the latter in mind, it's fair to say that Kryptonians are shown to be just as flawed and fallible as regular humans in spite of how we're perhaps meant to see them. For example, a character like Zod or Jor-El may exhibit emotions that run the gamut from joy to sorrow to hate, and still be described as mentally or intellectually superior. That right there tells you they aren't quite so perfect. Taking an even deeper look at what could potentially make an alien species like the Kryptonians better or somehow innately altruistic, it's important to note that our perception of reality especially as relates to man-made concepts like good and evil would have little to no congruity with beings possessed of physiological and psychological differences we couldn't even begin to understand. Indeed, those words, the very nomenclature behind them are probably ill-suited to describe what we'd actually be dealing with in a real-life first contact scenario. Having said that, it goes w/o saying that comic books and other fictional works usually require that their readers look on such incongruencies as essential trappings in a kind of literary sense. So, we just go with it. But even in doing so, our brains are still actively trying to discern between what's meant to be taken at face value and what's not. Case in point, as Kryptonians are consistently depicted in human form, we accept that this is intentional on the part of a designated creative team or what have you; they're, in fact, supposed to look like us. However, should these same characters carry on a conversation in English, as they're sometimes known to do, our reaction is notably different. Suspension of disbelief kicks in and we pretend that the language we're hearing is somehow Krytonian-based.
Similarly, whether it's because fans and more casual readers would rather not entertain all the complexities that come with taking a realistic approach to Superman's backstory (I briefly touched on this in the first paragraph), or simply because none of that's ever dawned on them in the first place, you'll rarely if ever come across a perspective such as this one outside a CB/CBM forum. I suppose that's for the best, though, as the discourse might spur a trend that ends with him looking like something out of
Arrival or
District 9. And no one wants that. lol Verisimilitude is preferable and has been achieved with varying degrees of success, but I still maintain that it's in the best interest of the big blue to stay true to the unadulterated fantasy bits that made him appealing to begin with.
Getting back to the main point, when you take all of the above into consideration, one thing becomes clear. While Supes naturally functions as an alien by virtue of his many in-story exploits, his characterization speaks more to the experiences of a human male, a kind and just human male with extraordinary powers, but a human male nonetheless. The same can be said of many religious and mythological pantheons when you think about it. Those Norse gods in particular, as they've come to be depicted by Marvel over the years, can be downright petty and cruel! Then you have a complicated character like the popular
The Boys villain, Homelander. What's interesting about Homelander is how often he gets compared to Superman even w/o having the extraterrestrial detail in common. Once again, this demonstrates that in the casual analysis of Superman's behavior, the alien component in his origin is all but inconsequential unless we treat it as a misnomer for superhuman, i.e., a regular person endowed with special abilities. Truth be told, that's what most people are doing anyway whenever they endeavor to deconstruct the hero, consciously or not.
With that stuff out of the way, let me quickly address Superman's relationship with Jon and Martha Kent. As we've already established that the details pertaining to his Kryptonian background are viewed in a way that's unique to how we relate with his more human traits, it's easy to see why the Kents would have played the most pivotal role in his moral development. But, of course, even those who represent the best in all of us are still susceptible to corruption, effects of good nurturing and the like notwithstanding. And as you previously pointed out, this is indeed true of Supes, evidenced by all the times he's gone rogue in the comics and elsewhere. Come to think of it, Hoechlin's Clark too, as he's sometimes portrayed on
Superman & Lois, has been the subject of criticism (undue criticism in my humble opinion, but that's irrelevant) in this very thread; his parenting skills being the impetus for that. All of this paints a picture of a man who's indubitably good, but not so good he can't ever succumb to his darker impulses. Granted, it should take a hell of a lot to get him there.
To sum things up, that Superman, at his most virtuous, regularly refrains from moving in a direction that would ultimately bring the world to its knees is a miracle to whom his adoptive parents should forever be indebted. By extension, what makes this particular aspect of the character so compelling—to me, at least—is something quite simple. He consistently challenges himself to do better, and contrary to popular opinion, that doesn't come nearly as easy to him as one might think. Like the Hoechlin version tells Jordan, you have your good days and your bad days. To get ahead of the bad ones, you have to always be at your best. And that takes work regardless of who you are or whatever it is that you're capable of. After all, it's in the struggle that we find our meaning and our worth. At any rate, to reiterate, I get where General Lane is coming from in the latest
S&L episode. It's mostly how he went about it that strikes me as imprudent.
So as Krypton’s backstory was fleshed out over the years, more complexity, conflict and flaws were introduced. For example (and as you mention), Krypton had criminals (Zod and co.) and a prison (the Phantom Zone). These conceits provided Superman with formidable villains. But it also diminished Krypton as the source of his moral wisdom. At which point, the influence of the Kents — and wholesome American Values, generally — becomes the more plausible guiding force behind Superman’s nobility. (Personally, I’m critical of many American “values.” So I’m happy to give Jonathan and Martha most of the credit. 
)
