I think as a business decision you would have to make the trade and trust that the Celtics environment and coaching staff can transform Melo into something more efficient and deadly as a player. Its a massive risk but one that might catapult the Celtics into contention immediately.
All that said, I am not a fan of Melo or his game as it is currently constructed
Melo is a career 45% shooter and 33% from the 3. Not really inefficient. Although, he is shooting 41% right now, but it's early.
And along that career 45% shooting is a career 25 points per game. If that's the problem the Celtics need to worry, then give to us.
Carmelo has a career eFG% of .480. That's decent (not great) efficiency for a primary-option scoring forward.
EDIT: Misread table. Will revise comment.
Revision: Carmelo has shot above .500 eFG only twice in his career and only once since 2007-08 (last year at .502). He has been below .480 in 3 of the last 5 years and is at .442 so far this season.
For comparison, Paul Pierce has a career eFG% of .499. And PP has not posted a number _below_ .500 except once (.499 in 2011-12) in the last8 seasons. He currently is shooting at a .566 eFG clip.
Since he's the topic of trade, we should mention that Jeff Green's career eFG% is .489. Notably, his number is dragged down by the low .441 he posted his rookie season. Since then, he has never been below .488 an has been above .500 since joining the Celtics. He is currently at .526 for this season.
Carmelo is a volume scorer. He is not particularly efficient one.
Green is an efficient scorer. He is not a volume chucker.
Carmelo is a bit underrated as a passer. His Assist rates are not anywhere near Pierce, but they are solid. And he's a pretty decent rebounder.
Those are two areas where Green does not measure up to those guys.
On the other hand, Green is a much better perimeter defender.
In the end, given his contract and his low shot efficiency, I am not particularly interested in having Carmelo on my team.