What can the Bulls offer besides Deng/Hinrich and if you're the Cavs, why do you want to give the Bulls more cap space? A S&T with Chicago only benefits the Bulls unless it's Noah or Rose, and if that's the case, LeBron's not going there without them anyway.
If the Cavs wana go get Deng and Hinrich and a late 1st round pick and get throttled by Rose/LeBron/Bosh/Noah every time they meet up, then well, I wouldn't even know what to say.
Only attractive options the Cavs would target in NY are probably 1 of Gallinari/Chandler to go with Douglas. So here, why take away talent from the team you're going to, to try to win?
Those young players (Noah, Gallinari, Chandler, etc) are assets to the Cavs in a S&T, but they're an asset to LeBron for winning on his new team.
I think Miami's a different scenario and would be the only case of it working out because Beasley still could be valued and he's not expensive, and he's not really an important piece that LeBron/Wade would need.