I still think most superheroes are oddly selfish, like seriously- using random cars as weapons? Plenty of heroes kind of act like that they can do whatever they want because they're "heroes" and really don't seem to care why being a vigilante is illegal. At most they're all "I'm not like that". Superman is probably one of the worst in that regard, as he refuses to legalize his actions and the Justice League is often considered an NGO Superpower because they barely care about acknowledging the world government. At most they're clearly unhappy about people trying to limit them. Like if it doesn't seem alive, they're often willing to kill "just because" and high-tier ones like Superman have no need for a secret identity. Sure, he shouldn't be forced to Superman 24/7, but when he isn't on the "clock" he tends to ignore problems. People like Superman are heroes with undeserved respect, who aren't violent- just careless and indifferent when not dealing with something that is their "immediate problem". I think that's the reason Lex tends to get fed up with Superman- dude is ridiculously powerful, but never worked for any of it. Dude saves a cat from a tree and suddenly gets a ton of rep for being "a real superhero". Even Superman doesn't see a problem with his behavior, even though he should feel guilty for all the inaction he did. It is really only ever just Superman Lex tends to be offended by, and the only real distinction is that Superman is someone powerful who wastes his own potential to play reporter.
This is like the least charitable interpretation of information possible. In comics people don't constantly use random cars to a ridiculous degree. I like to use it in writing because it lets me demonstrate superstrength in a way that's more interesting to read about than "he punched really hard", lets me change up the flow of a fight and allows me to demonstrate some intelligence on the part of the combatants (if someone got pushed back far by another powerful opponent and they hurl a car at the person who pushed them back it lets them demonstrate some more lateral thinking beyond "run at the other guy and hit them" which makes the fight more interesting and engaging as a result).
Your second point is straight up wrong. Superheroes do care about why vigilantism is illegal. Batman for example has straight up said on multiple occasions (including in the DCAU) that he's working specifically so that there shouldn't be any more vigilantes in the future and that in his ideal world there would be no need for Batman in the first place. The problem is that most superheroes see the existing power structures as fundamentally incapable of achieving what they want to get done. With regards to the Justice League not caring about being an NGO superpower, there have been multiple Justice League and Society teams directly under US supervision (generally whenever they stick "of America" in their title), there are entire storylines about Justice League interaction with the UN, the Justice League has disbanded over concerns that they have too much power and don't have government oversight and much, much more.
The heroes who do choose to destroy things that don't seem alive aren't usually doing it "just because" so much as a philosophical reason regarding the sanctity of all life. Whether you agree with that philosophy or not is a different matter or not but it's not often something super pithy. Furthermore plenty of superheroes (Green Lantern, Huntress, Captain Atom, Wonder Woman, the Doom Patrol etc.) will kill even if they're not murderhobos for justice.
As for Superman's inaction, part of that is because Superman doesn't want to be someone swooping in to save the day on every little thing and he can't actually fix everything. Sure Superman could conceivably stop a war from brewing in say the middle east, but he can't fix the underlying tensions and reasons for the war in the first place so much as engage in delaying action. He can't stop people from being put into conditions that make them want to commit crimes, and its not his responsibility to do so and fix everything. Sometimes you have to let people solve things on their own.
Furthermore the idea that Superman just pulls cats out of trees and gets praised as a real hero is an exaggeration at absolute best. He generally takes down very powerful supervillains who threaten cities, if not countries or the entire world. What he does doesn't fix more long term problems like wealth distribution the world over but it is also significantly flashier than say a stimulus package designed to help people get on their feet in ten years time to hopefully reduce crime. Yes Lex can resent him for being praised as a real hero when he is not and he does have something of a point (even if it requires ignoring the fact that Superman is not trying to fix everything ever so much as deal with things he feels he is uniquely capable of dealing with that the normal systems would struggle with) but what you argued for is a ridiculous exaggeration.
There is some critique to be made of superheroes (perfect paragons are often uninteresting to read about which necessarily means that superheroes must be flawed) but at a certain point the critique of superheroes shifts away from a critique of the characters and more to the nature of the genre itself. You can argue that some superheroes are selfish and shouldn't be praised as heroes but the argument you presented above kind of doesn't work.
I feel that is a good point superman is very willing to play judge, jury and executioner like darkseid in comics (something about singing him to death) darkseid in the cartoon by throwing him to his slaves saying u deal with him, zod (in the orginal movies and man of steel issue #22 of Superman vol 2) granted these guys are dangerous but their is a reason supes is the one who seems to snap first
Not really. You have maybe two incidents of him actually doing this in the four examples you listed. Darkseid is a quite literal god of evil and is immortal so Superman fundamentally cannot kill him. Ignoring that when he was singing him to death it was literally a crisis scenario where the options were "let Darkseid conquer the entire multiverse forever" or "kill him" and Darkseid had killed Batman beforehand (or at least it seemed so at the time) which I imagine is kind of a unique instance that is not a normal circumstance for Darkseid, and in the DCAU he very pointedly did not kill Darkseid when he threw him to his slaves and he knew that this was the case. It was supposed to be a "you reap what you sow" moment from Superman after he had beaten Darkseid to near death after Darkseid had brainwashed him to make him attack earth, beat his cousin to near death and fundamentally destroy most of the goodwill he had built up. The slaves then carry Darkseid as he pithily tells Superman that he is many things but on Apokalips he is god and Superman then flies off leaving Darkseid. So both situations are extreme outliers and he straight up didn't kill Darkseid in one of them.
Now I'm not familiar with Man of Steel issue # 22 so I can't talk about it there so I'll assume it's salient (though if it's anything like the movie Man of Steel where he also killed Zod there was huge fan backlash over Superman acting out of character and an attempt to force Superman into a trolley problem to justify the decision to kill Zod). In the 1980 Superman 2 movie he does kill Zod after Zod overthrows the American government, this is true. However it's a one off thing from a movie 40 years ago. Batman brands people in the old WW2 era specials and he straight up carries a gun in the early comics. Yes the movie came out significantly later but even if we take the most extreme angle and argue that this was relevant to his character in the 80's (it wasn't) we can still make the case that Superman's character has sufficiently diverged from where it was 40 years ago. Furthermore Batman also killed even more people in the Tim Burton movie that came out almost a decade later, but no one is seriously attempting to argue it as evidence of "Batman is totally willing to kill people" because it's excused as being part of the movie adaptation.
Now to add all of this up you've got maybe one example that holds ground. You could bring in other examples of when Superman killed villains (like Doomsday or Parasite in the Man of Tomorrow movie) but it requires you completely ignore the circumstances behind what happened (in the fight with Doomsday it was a mutual kill and Superman literally died fighting him and in the movie he accidentally killed Parasite by overloading him if I remember correctly for example). By and large there are almost no good examples of Superman playing judge, jury and executioner and for the most part it's about as relevant as saying that Batman uses guns (Batman has used guns in his earliest comics, he shot Devil Ray with a gun when possessed by Deadman in the DCAU and in the same crisis where Superman supposedly killed Darkseid Batman picked up and used a gun to try and take down Darkseid first), reliant on ignoring circumstance and piecing together disparate occasions to make a bad faith argument.
The perception of Superman being willing to murder people is probably an unintended consequence of people being terrible uncreative writers and constantly throwing evil superman into a bunch of stuff because they're hack writers who can't come up with anything interesting or original and have been steadily writing worse and worse evil Supermans than Frank Miller did back in the 90s. Superman's not really a murderous individual and considering that in the 70+ years he's existed you can still count the times he's overtly killed a character across multiple forms of media on your hands, I think it's safe to say that Superman killing people is by far the exception to the norm.
