I know he's the most violent (not counting Damian who of course is a child sociopath with blood on his hands) of Batman's protege's and certainly he's not the most stable. However one thing that always stood out to me is that as a Robin he never kissed up to Batman and their relationship involved a lot of disagreeing. From what I understand this is why he wasn't well like because he often talked back to Batman and they did not always get a long. I have not read much of Red Hood recently but I have always felt a good direction would be for Jason to become the kind of person Batman would like as a successor but to not want it and to become very critical of the way Bruce does things.
I mean Bruce/Batman takes orphans and takes them out at night to fight serial killers and criminals you can't tell me that does not have a negative affect on their minds. I'm surprised when you consider the lunatics Batman faces like Pyg, Zasz, and Joker that more of his proteges aren't like Jason. I've always felt like a good direction for Jason Todd would be for him to become a cop that actively opposes Batman and actively tries proving Gotham does not need him. I mean I feel that would be interesting to see Jason go from vigilante to reformed GCPD officer out to take the Batman Family down(as a rival to Batman and his methods) because he feels Bruce/Batman does more harm than good.
I feel that would be a good dynamic Jason and Bruce butting heads and arguing over what's really right and what wrong. With Jason deciding to stand for something indisputably good while opposing Batman completely. Especially since Jason wouldn't be entirely wrong.
As a cop Jason could still use lethal force when necessary and not much would have to change with him. I think Bruce's reaction as well as the rest of the Batman Family's reactions would be interesting to especially if Jason made such a big change and actively started putting Batman on the spot like how Damian has been known to kill it would be interesting to see Bruce react to Jason putting him on the spot for tolerating that calling him out on how he does nothing about that kind of behavior. I think of all the protege's Jason becoming a character that grows to believe in the law when it comes to crime fighting but actively opposing and being critical Bruce's views and methods would be sort of poetic. Since he's had the most unstable background I think it would be interesting if without Bruce he actually became more stable and surprisingly well rounded.