But the big differnce is Barbara could be a Titan, while Kori simply doesn't work in typical Batman comics.
And Dick will never be that removed from Batman that it would make sense for him to stay completely out off all big Batfamily events.
Even back in NTT you had imo the problem that Dick didn't worked that well in the Kori centric space stories. And the more detective centric stories where Dick could shine were usually ones were Kori was out of the picture.