Wayne enterprises apparently encompasses stuff like defense industries and medical insurance; if someone who'd been denied healthcare insurance and was either dying or slowly watching their body die or fall apart on them killed Bruce in a similar fashion, how would his friends react?
Superman, the flash and even green lantern are portrayed as fairly understanding people (although Superman and Batman are literally best friends), but Wonder woman is decidedly not; thing is, if they found the shooter, some guy who could barely walk, perhaps shaking from whatever ailment that progressed because his health insurance decided to delay as long as possible (with the likely intent of waiting the guy's health out), what would they do? It's hard for me to imagine even Wonder woman hurting some guy who can barely stand, even though she's definitely one of the DC heroes who kills her enemies (or at least some of them).
I'd ask what if it was a person from the global South who'd been a victim of Wayne enterprises' defense industries but honestly given DC is an American company, I can easily imagine Western heroes pounding the heck out of an Arab or African person who'd lost loved ones to Wayne enterprises.
Those superheroes aren't really vengeance driven aside from Batman. They'd probably let the police pursue them.
If we're applying reality to Batman, which I was thinking about the other year when watching Gotham, is that you have to consider multiple things:
The Wayne parents, that is, Thomas Wayne and Martha Kane acted in ways that did not fit their bourgeois character and intelligence. They should have exited the opera through the lobby, wait for Alfred to pick them up, and then leave via their car. Also, billionaires still have private security when they do travel for outing/events and would not leave security up to an old SAS soldier but have multiple guards to protect them. In crime-ridden Gotham of all places. Even if Bruce was annoying them, people like the Waynes would know and act better. The Waynes were deliberately reckless in the Batman mythos.
Bruce, as the son of a billionaire, despite being an orphan and his mother's family being the only ones he had left, would still not have been as isolated as he would have been to indulge and sulk in his parents' murder. Bruce would have been integrated into his family's bourgeois circles of connections, friends, and family as means of surrogate fostercare and groom him to succeed his parents as bourgeois giants.
Alfred was legal guardian of Bruce. Despite his sympathies for Bruce and wish to indulge him, Alfred would have been pressured by the bourgeois circle of Gotham and the state to put Bruce into trauma counseling, boarding schools, and away from his parents home and tomb.
Gotham itself would have eventually self-corrected through bourgeois discipline, i.e: capital flight, divestment, and strikes from municipal bonds. I think the story gets away with this by making Wayne Enterprises a monopoly on the city, insulating the city from capital discipline, but corruption and crime still scare away investors and Wayne Enterprises would have eventually shrank enough for other financiers or industrialists to crowd out the rent-seekers like in the Court of Owls.
This still wouldn't stop the national and international bourgeoisie and state apparatus to discipline Gotham. A capital strike on municipal bonds would starve out the city of funds and connections to the state and federal governments would pressure investigations and emergency managers to subdue Gotham, as well as bring in a national guard as police/clean house of corrupt judiciaries. RICO became a thing for this reason. Tangentially, this type of crime-ridden hellscape city would drive out high/mid income earners into the suburbs or other cities. Labor flight & brain drain would happen too.
Alan Moore's Watchmen and Killing Joke satirizes these superheroes well. They're good reads.
Man I'm not nearly intelligent enough to understand most of this; I just wanted to know literally if Superman broke down the killer's door and saw a frail, disabled man, what would he do (Superman, or most of the justice league).
If we were going to look at this literally, one could also ask why all these powerful criminals insist on operating in Gotham when so many other cities would be safer (there's far less superheroes than there are cities; there's also other countries). For instance why is the penguin, a corporate and political kind of evil, insisting on operating in Gotham? He also absolutely would have taken funds from AIPAC and Batman would be called anti-semitic if he opposed the penguin on the basis of taking funds from AIPAC.
I just wanted to know if the JL would pick the suffering people even if those people had killed one of their closest friends and ally.
Gotham sits above a Lazarus Pit, which is partly why there's so much crime to begin with. Groups like the League of Shadows know about it, which is why they continue to invest in taking over the city. In some canons, Bane's strength enhancing drug is made using the Lazarus Pit.
This has an affect on the rest of crime in the city. The groups vying for control need funding to fight each other, which means drugs/guns/racketeering/gambling/prostitution/legitimate businesses to act as fronts in order to bring in cash.
A pretty consistent thing is that Bruce does have connections to all the other diletantes and cultural and financial elites of the city. He actually has a very wide social circle. It just isn't very deep.
And a hostile bond market and divestment form the city wouldn't have corrected Gotham. You can't lack of investment your way out of the joker.