To start, it isn't mine.
Second, any discarded equipment becomes part of the field. Therefore, moving it means the umpire is reconfiguring the playing field
Third, if the umpire moves a bat to another location and that DOES effect the play, who is going to be wrong there and if it results in an injury to someone, who is now liable for putting the equipment in a place that it would not have been had it not be relocated.
Fourth, the umpire should be watching the ball, fielders, runners and bases and moving into the proper position to make the pending call. Shouldn't be searching for or looking at a piece of equipment that is fine where it is. If the players want to move it, they can, I've got other responsibilities.
Fifth, if the umpire picks it up and then must move whether to avoid the play or make a call, who is liable if someone gets hit with the bat in the umpire's hand.
And I'm talking about all equipment, including the ball. This is why umpires are directed to not take a ball from a fielder at any time. What if the ball is live and the winning run is rounding third and F3 mistakenly tosses the ball to the umpire who is now standing there with a live ball in his hand as F4 is trying to take it away? No matter what happens, from this point it is going to be a mess.
Real simple, just like you would tell a younger sibling, you don't touch my stuff and I will not touch yours. Keeps everybody happy and out of trouble. Want to be a nice guy, go do volunteer work.