Why the Bulls might do this: They actually dump salary in this deal. I know that the repeater tax is coming up for them, and they are currently paying just over $7 million in taxes. With the repeater penalty, that comes out to like $18 million next year or something awful. This deal lets them dump $6 million in salary while still acquiring an all-star caliber player in Melo, and a plus defender in Shumpert. For a (much, much) better analysis of the Bulls' upcoming tax liabilities, read this wonderfully written article.
The Knicks aren't winning this year anyway, so why not let injured Derrick Rose rehab and be ready for next year, right? Boozer's contract comes off the books in 2015, so this doesn't affect those plans, and he's essentially Bargnani with more rebounds and less threes, so you can play each of them 24 minutes per night without really losing anything, or you can play them at the same time with Chandler on the floor and see what happens.
In this scenario, I'm just assuming Amar'e will be injured again very soon.
Then next year, the Knicks have a lineup that looks something like:
Rose/THJ/Metta/Bargs/Chandler or if Metta's gone, you could go Rose/THJ/JR/Bargs/Chandler. That's enough shooting around Rose to open up the floor for his drives to the basket, and Chandler's a great PnR finisher. And with Amar'e/Boozer providing mid-range jump-shooting and average level rebounding off the bench, the second unit just needs a good point guard (one more year of Pablo?) and the team could actually be pretty fun to watch!
Add to that, the fact that Boozer's and Amar'e's contracts would both be large, expiring deals, maybe the Knicks can get an extra draft pick or two from a contending team next season and wind up getting two or even three shots at the first round in a loaded draft.
I don't know. I'm just playing around with the trade machine at this point, but I thought that might work. Especially with Shump being a Chicago guy.