The funny thing is there are a lot of ways this could work, and none of them seem to be on display. Like you could make a pretty good deconstruction of the teen sidekick trope. After all putting teenagers in dangerous situations where violence will ensue and death is possible is going to fuck people up. Like instead of Robin being all "Fuck Batman" edgy teen rebellion focus on the fact he's a child solider. People get hurt and even die in fist fights all the time. If someone acted the way he did it's inevitable that someone is going to end up dead. By sheer odds someone is going to get a skull fracture or suffer internal bleeding and die. So use that. With Raven she's literally the anti-Christ who wants to save the world. Her comic character is filled with angst and drama just ready for the mining. Beast Boy turns into some of the most dangerous animals on Earth. There's no gental way for a Grizzly Bear to hit someone. He's going to kill people all the time in a fight. Not to mention the fact that everyone he's ever loved has dead or abandoned him. His jokes are outright said to be a coping mechanism to deal with his trauma. StarFire's life is Game of Throne's meets Star Wars. It wouldn't take much to get a Watchmen like subversion of the genre to really take a look at what people like this would be like in the real world.
Or on the flipside turn this into a dark comedy like Deadpool or Rick and Morty. Like if the idea is to say Suck It to people who say DC is too dark, play into that. Have dark violent shit happening and have the characters just play it off. Don't take the darkness seriously. Have the Titans joke about how fucked up this all is, how silly and absurd it is that they're a bunch of kids in tights fighting mob bosses with stupid names selling drugs on playgrounds. Laugh with the audience. Look at Teen Titans Go, it's not a great show, but it's dark as hell. Despite the color scheme the show is full of violence, death, and the heroes are major sociopaths who are unable or unwilling to learn from their mistakes. Play on that theme and explore the insanity these characters exist in while being just empty violent sociopaths who are giggling their way through the void.