enough money, highly qualified personnel, and connections (both legitimate and clandestine) to bring real change to a blighted city
does none of the sort
He does use those resources to make change through charity and programs designed to improve the community. But that doesn’t instantly solve existing crime, particularly organized crime and corruption.
Plus, it will never actually fix Gotham because Gotham being shitty is part of the premise.
brutalizes mentally ill people (but it’s okay because he doesn’t kill)
He beats up violent criminals, generally when they are in the middle of either attacking him, or attacking someone else, or otherwise doing something that would harm or endanger innocent people. That some of these people have varying degrees of mental illness is unfortunate, but they doesn’t mean they don’t have to be stopped.
crime lords and terrorists walk free because of notoriously terrible corrections system and no-kill policy
Everyone of those criminals who walks free could have just as easily been murdered by any number of people during their time in custody. Why is it Batman’s responsibility to decide who lives and dies, and not any given cop or prison guard? And even if the system is broken, is it really better to have a masked vigilante killing people without trials (and appeals, and evidence, and oversight by some kind of authority)?
Also, let’s be real here, the reason they get out so predictably is not because of in-universe reasons, it’s because they want to keep bringing back villains. He could kill every supervillain in Gotham and most of them would be back in six months.
main appeal is cool gadgets made by other, more qualified people
He’s the world’s greatest detective, a ninja, a world class martial artist, a scientist, an inventor, and one of the greatest strategists who ever lived. If he’s not qualified, who the fuck is?