I think they have just over done it with making him "safe".
I mean there are plenty of examples where they had Batman or other Family members team up with more anti-heroic characters, were it worked without a problem and without taking away their edge. Like Batman and Ghostmaker (or even Catwoman), Dick with Tiger or Midnighter, or how Huntress was often written before she joined the BoP.
I think even Jason's team up with the Outsiders in the recent One Shot, is a good example how you could do it properly.
But usually when he is arround the Batfamily the writers never really let him do anything morally ambiguous, or really any thing lets him shine. He is usually mostly used as jobber or comic relief, or to make other characters look good by comparison.
And that's imo damaging the character on the long run.