Is cutting the arm off the Z-axis switch a good idea?
While I haven't seen this on a Z axis for a printer personally, there is no reason it wouldn't work, and would improve your repeatability in theory. Removing the arm on the switch is taking away the lever. Going back to simple machine mechanics, the lever gives you a larger range of motion in which the button could be triggered, with the tradeoff that you get a larger target to hit. How much of an improvement depends on the exact switch, where the button is compared to the axis of the switch, and how long the switch is. 

My Shapeoko 3 CNC router has a switch for all three end stops that do not have arms, and my Original Prusa i3 mk2 has switches without lever arms on X and Y axis endstops, so there is is no reason it won't work for your i3 Z axis, you just need to make sure you can accurately hit the small button on the switch.