Yes, I could mount the bender to a board, but it wouldn't be as portable as it is now. I can bend stabilizers in my office, by the dining table, wherever around the house. If I bolt it down, I am going to be stuck in the garage when I make stabilizer bars. The wire is not that hard so it is fairly easy to bend without bolting the bender down.
Also, the few times in the video when the bender was moved out of sight, it is because I needed to bring it up so I can eye ball the wire's angle, make sure it is either flat for the 90-degree bends or at the correct angle for the Z bends.