One big reason why Green tends to stand in the corner a lot, which is not necessarily a bad thing since he's hit the corner threes at a very good rate, is that he's not a pick and roll ball handler. His offensive game besides spot up shooting revolves around isos and the lowpost. Not only is this team not built around clearing out for Green repeatedly but the production they get from doing so isn't all that great.
There has to be a way to get Green easier looks. When he's given the ball in the post or on the wing and asked to create, the shots are almost always difficult and highly contested. He doesn't have the crafty ballhandling or quickness to create separation.
I'd like to see Green play more alongside Pierce on the wing. Maybe it wouldn't benefit Green individually but Green's size would force teams into a difficult decision of who to put their smaller defender on. If it's on Green, he'd be in better position to use his post game.
Regardless of who guards Green, a tall or small defender, he's not going to create a lot of horizontal separation. He even struggled to do that against Hawes. Maybe another way is to create vertical separation by trying to get him matched up against shorter guys. He would have more room when he gets off lowpost shots and pull up jumpers.