Every association I work with has told us to leave the bat alone. The bat becomes part of the field after it leaves the batters hands. If the catcher wants it moved, let them move it.
Several reasons have been brought up, the main one being the liability issue. If you move the bat and then someone trips over and is injured, more than likely the blame is going to go on the umpire for having moved the bat. I was also told of a case where an umpire kicked a bat out of the way and then was blamed for damage to the bat and a claim filed against him.
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