He's only inefficient because a) he's always had to do too much offensively b) he's ALWAYS been the #1 scoring wing/perimeter player c) never played with a great PG d) never played in a ball motion offense.
It's no coincidence the seasons where he had around the same touches as OJ, he shot 47%, 46% and 45% respectfully. The following seasons his scoring load increased, therefore it's only logical that his percentage dropped. It's amazing that even though he had a competent secondary wing scorer his %s were that high, given he still was the #1 option and had to create his shot mostly from isos. With perimeter touches from Rose and Butler, he's going to be either the 2a or 2b scoring option; he'll be able to pick his spots more regularly, he won't be forced like he was previously to conjure something up from nothing (which either directly or indirectly led to him jacking up shots, out of necessity and habit) for the Bulls, because his role won't demand that on the regular.
More often than not, he won't have the best defender guarding him, he won't see as many traps/doubles/help defense as he previously did in Memphis/Toronto. He will LEARN to share and move the ball, because he'll no longer be the #1 guy.