You're absolutely right. The bulls were successful this season because no other teams outside of miami had a 6'8 monster who could legitimately guard (possibly) the fastest PG in the league but they just suffocated Rose last night and the bulls couldn't do shit about it and couldn't create offense elsewhere.
Its hard to say but I see both sides of this. The bulls needed someone who could drop 20ppg and can create his own shots to draw defensive big men away from Rose but Boozer certainly has weaknesses. With Deng, Noah, Asik, Thomas and Gibson's defense this was rarely a problem during the season but the weakness is exploited by Miami by having Bosh out there alongside multiple players who can effectively penetrate.
It'd be nice for the bulls to still have that cap space but there's no guarantee they'd get a better option and although they did pretty well while he was out, its really difficult to determine how they would've fared overall this year without him.
They still have a defensive identity but if they just played Gibson, they'd be slacking even more offensively and that would only compound the problems they faced in this series getting offense outside of Rose.