With no outs and runners on 3rd base and 2nd base, the batter grounds deep to the shortstop, who throws to 1st base. The runner on 3rd scores.  The runner on 2nd moves to 3rd base. The batter is safe on a close play at first, but the batter carried his bat nearly all the way to first base and dropped the bat (actually threw it a short distance) towards the first base coaching box as he was about to touch first base.

 

The defensive coach wants a penalty. Sound reasonable? What does the umpire do?