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While there are legitimate reasons to trade Haslem, the Heat should hold on to the two-time NBA champion.
He is a great rebounder, which the Heat very much need, and while he's certainly overqualified for his role as a 20-minutes-per-game substitute, that's not necessarily a bad thing.
Also, Haslem and the Heat have a special relationship. He's spent his entire career in Miami. Dwyane Wade, LeBron James and Chris Bosh all took less money in 2010 so Haslem, who also had a better financial offer from the Dallas Mavericks, could stay with the Heat. And this relationship doesn't stop with the players. Pat Riley attended his mother's wake.
Trading Haslem would have a huge negative emotional impact, and that clearly matters. Look what happened to the Boston Celtics in 2011 after they traded one of their tone-setters and emotional leaders in Kendrick Perkins (33-10 before trade and 23-16 after).
Haslem hasn't played great so far. However, there's too much risk, from a pure basketball standpoint and an emotional one to trade him.