The short answer is that Jason Todd should still be dead, the long answer is that he works best as a villain except being a villain is maybe the single worst choice you can take with the character.
Jason Todd died and then Batman let his murderer go free, and there's no degree of "Batman is as crazy as his villains" to justify letting the guy who beat your son to death with a crowbar get away with that. This is already bad enough, but now Jason Todd is alive again and asking the extremely sensible question "why the fuck did you let him live when he killed me?????"
So now you've got a character who, in his entirety, exemplifies the absolute nonsense of the Batman mythos, This is a riveting take if you're 35, extremely boring, and need your children's pulp fantasy characters to apologize for their own premises and fortunately DC writers these days have managed to overcome these horrible deficiencies in a time and place where Jason Todd has comfortably settled into a roguish heel of the Batfamily, and it's his absolute best placement.
First and foremost, it's as simple as this: If Batman's son, who he failed completely and utterly, was running around being an evil jerkface, every Batman story devoted to him not doing every single thing in his power to reform him and bring him back into the fold is officially less important than what he should be doing instead. Jason had a hard life, died, and then he found out no one gave a shit; there's absolutely no way to portray him as anything but an entirely sympathetic victim of circumstance and, as such, he needs to be one of the good guys, because if he isn't, then the good guys are failures for letting him down.
Moreover, a villainous Jason Todd who shoots bad guys with guns and is mad that his dad let him get murdered with no consequence to his murderer sure sounds fun, but it has a huge problem: this franchise is called Batman, and it's centered around Batman's ideals (that writers keep failing by showing those ideals as weak, stupid, and ineffectual, but that is what happens when you listen to middle-aged people who want their cartoons to grow up with them), and so there is no way for Jason Todd to meaningfully confront Batman's ideals where he will in any way succeed, because every single thing an evil Jason Todd wants to do is in direct opposition to shit the Batman mythos has hammered in for decades. Even if you want Jason Todd to exist as your vector to go "why doesn't Batman kill the bad guys like a cool adult" he will never ever ever ever ever succeed at this, so now he's here to literalize your dumb stupid fanboy arguments that suck every single ounce of joy I have ever felt reading about these characters.
Jason Todd right now is a good guy without question. He's roguish, he's edgy, he'll stomp off and go do what he wants, but he's always going to be in the Batfamily because he belongs in it. There's tons of mileage to get out of someone who lives up to ideals that failed him, and how he copes with the aftermath, which is why I'm a huge mark for Jason using guns: It's his way of going Fuck You, Dad, and you can futz around with rubber bullets and "shoot non-vital areas" to sell that Jason is making a big posturing statement in defiance of Bruce's rule while still being a good guy, which works entirely because even if this is Batman's corner of the universe, it's still bigger than him specifically and plenty of hero characters use guns. Jason follows those ideals his way, and there's no Batman character better suited to question and challenge them than him, because like Bruce and Cassandra Cain, Jason is a character defined by the taking of a life, it's just that the life taken was his.
