I guarantee you Boozer would not complain if he had to play with Carmelo Anthony instead of Noah. It is easier to find rebounds than it is to find 28ppg scoring wing players. The team, as constituted, is not good enough to beat the Miami Heat.
I actually disagree with you. I think rebounders of Noah's caliber are more rare than players who can put up big numbers in the Pts. part of the boxscore. What the Bulls ideally need is a guy who can play off-the-ball well to complement Derrick Rose and Boozer in the screen-and-roll game. Deng is a pretty decent piece. Maybe not offensively ideal as a guy like Ray Allen, Rip Hamilton (pre-injury), or Michael Redd (pre-injury)... but he has a mid-range jumper that is about automatic if you give him space.
If you trade away Deng and Noah for Anthony, you lose trade leverage, depth, and you lose one quality starter. You also will need to depend on Boozer to cover the middle... and he gets destroyed on the glass by most taller Centers in the league. That is exactly what happened to the Jazz (ranked #1 in the NBA last season in rebound differential) when Okur went down and Millsap and Boozer had to go head on with the Lakers' 3-man rotation of Gasol-Bynum-Odom. Their shots were getting swatted away left and right... and they were demolished under the glass.
Amd who is to say that NJ will give up a lot for Melo? Murphy and Favors was the last offer I saw that they had on the table. Is that better than an offer of Deng-Gibson-Johnson? I don't think so... NJ won't give up anything valuable because then Melo won't agree to a sign-and-trade with them. DEN's best option is to take whatever the Bulls want to give them, or to just seek out a couple other wild-card teams.
The Bulls already have Rose on the perimeter who specilaizes in scoring with the ball in his hands. He and Boozer will make the Bulls one of the best scoring teams. And Boozer and Noah would make the Bulls probably the best rebounding team in the NBA. Thibodeau is going to have them working tail on defense, as well... Why should the Bulls feel inclined to give Noah/depth/trade leverage away? They can always scout young talent, and trade Deng away for solid young prospects in the not-too-distant future. Rose will be one hell of a leader if the organization can manage to mold him into one. Look at Durant in OKC... he's only 21, also... but he carries that franchise... Rose can be the same way. Melo would be great, but for Noah? Big, big sacrifice...