Among all Celtics bigs (and I'm not counting Green, whom I don't view as a big), Wilcox is the fastest, the best in the open court, the best leaper, the best finisher, and has shown over his career—when given a high number of minutes consistently—that he's a capable rebounder (a rate of about 8 per 30 minutes).
This is pretty much my point above. Over much of his career, he's shown flashes of the talent that made him a high draft pick, but no consistency, and the production never came on a winner.
But...in 30 minutes, he could perhaps produce 12/8/1 off the bench. Surely he could be the difference maker if he could do that with any consistency.
Since we have a pretty solid rotation at the other positions (3 guards, 2 SF's) and need a 3rd big with Bass and KG, Wilcox the impact player in the 8-player rotation puts us in the running.