Gotham was always supposed to be shrouded in a sense of nihilism. That’s what makes Batman more important to his setting than arguably any other hero. Do the people deserve him? Probably not, but I think your Wonder Woman point about it straight up being TOLD to her that people don’t deserve her plays with Nolan’s Batman universe as well. Wayne/Batman recognizes that his efforts are largely thankless as the people of Gotham ostracize him to a certain degree. I’ve always felt that Nolan was trying to paint Gotham as place that could be essentially hopeless, but without meaning that it isn’t worth trying to save anyway. Whether or not you want to make real world applications to that idea or not is fine, but I like to always come back to the idea that we are talking about a rich guy dressing up in a bat suit at the end of the day.
The bleak and hopeless tone and nature to the Dark Knight films can get exhausting to some I suppose, but that’s what the Batman universe seemed destined to be. Batman was arguably the darkest comic book series even before Nolan came along. Name another comic book character who goes up against truly sociopaths like Batman does. Very few Batman villains seem to act with ambitions of “taking over the world” or something to that nature. Each of them all have elements of psychological terrorists who want to do just that, spread fear. I think Nolan recognized that and that’s why he created the Dark Knight universe in that image.