The Heat are certainly not soft in the paint, we just don't have size.
I agree with STDiva, Howard wouldn't put the Bulls over the Heat. The only thing he would bring is rebounding, but the Bulls are already a great rebounding team (not really addressing an issue). If you lose Deng, Lebron would just continue to have a field day.
He also brings scoring in the paint, he's a legit 20 and 10 guy something Boozer isn't. You're missing the most important thing though, that Howard would be the second option that Rose desperately needs. On another team he would be the number one player but on the Bulls he's the second option, that is just scary. It is also a matchup that has the potential to utterly dominate the Heat, whose greatest weaknesses are at point guard and center. Rose and Howard together would be a tandem the likes of which we have never seen before. A dynamic young point guard with incredible explosive strength and poise, and a young center hitting the prime of his career, currently averaging well over 20 points and 10 rebounds every night. They would have to go down as the Miami Heat's equals in the title chase.