Why not go to the bench during the disgusting 2nd OT?

The 2nd OT featured some horrible basketball.
After Paul Pierce opened overtime #2 last night with a three-pointer, O.J. Mayo made a layup at the 4:05 mark to make the score 108-107 in favor of Boston.  Then for the next three and a half minutes, nothing happened.

At least nothing worth watching.  The play resembled the type of thing you see at the end of a long day of playground pickup games when nobody runs anymore.  Jumper after jumper clanged off the front rim (10 consecutive missed shots by both teams combined).  I sat in the stands begging for Doc to call a timeout and stop the madness.  Eventually Rick Carlisle did (after 2:32 straight of atrocious basketball without a whistle), and a few possessions later Rondo finally scored on a drive to the basket that ended the drought with :35 seconds to go.

But my question is this: Why do the starters have to play both overtimes?  They all looked dog tired (Rondo logged 53 minutes, Terry 48, Pierce 44, and Garnett 40), and clearly were not being productive.  Why not sub in some fresh legs and see what they can do?  Lee?  Sullinger?  Wilcox?  Maybe even Barbosa (DNP, CD)?   Best case the bench brings in energy and gains valuable confidence and experience while leading the C's to a dramatic victory.  Worst case you drop a mid-December game that probably won't make much of a difference in the long run.

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