Well, we didn't trade for him when Miami got rid of him because we didn't have cap space. He got traded for a second round pick because the Heat needed to create cap space, and the only way to do that was to send him to a team that had the cap space to absorb him.
I'm not really sure how good of a fit he is on the team as currently constructed. He would basically come here and be the backup PF now that Bass is starting, with Wilcox playing exclusively at center. Beasley would probably play 15-20 minutes a night. He'd help us with bench scoring / shooting, but I doubt he'd help much with rebounding or inside scoring late in games.
The main motivation I see to trading for Beasley is to get a look at him this season, see how he can fit in with the culture, try to sell him on staying here and working out his issues, and then signing him this summer to a reasonable deal.