It's possible that Ainge made the move because he didn't put that much stock in Perk's game. This notion that Green was the centerpiece of the trade and should get big minutes because of it alludes me. His production and adaption to the system will warrant more minutes.
Nobody is arguing that Green should get minutes out of charity or to save face. However, if Green is good enough to trade a starter off a championship team, it stands to figure that the team thinks he has some value. He should get the minutes to prove it.
(I don't think the argument that Danny traded Perk because he didn't think Perk had a lot of value is legitimate. Danny is smart enough not to tamper with championship chemistry for a guy who can't play. I think Danny undervalued Perk's intangible contributions, but even so, he's not a total idiot.)
As for a KG/Green lineup, it's not going to work in every matchup, but the ability to go small is one of the strengths of this team that isn't being taken advantage of, mostly because we don't have a healthy center who can rebound and defend the paint. KG is the only guy capable of doing that in a small ball lineup right now.