I was taught not to touch the bat - and that has been reinforced at every clinic I have attended when the subject came up.
Not just because of playing reasons, but mainly because the umpire is meant to be doing other things. On a deep fly ball you already should be out towards the circle to get a view of the catch, and then you are moving into position to ready for possible plays at third or home (depending on the situation) - all while keeping track of where the ball, and where the runners are so you can predict what could happen and be ready to move. Not stopping that to move a bat.
Exactly. Some of the umps we get are a bit... err... portly... and I could see them bending down to move a bat and not recovering in time and getting plowed over as part of the play at the plate.