Jason might've worked better from the start if he'd always been the post-Crisis street thug version. As I recall, he was pretty loathed because he was so clearly a Dick Grayson surrogate.
(Then again, A Death in the Family was kinda fixed, if you think about it, albeit unintentionally. The Dark Knight Returns had come out a couple of years prior, and wasn't yet definitively considered non-canon. And it specifically states that Joker had killed Jason years before.)