I don't think there is a great need to move the lights.
The major benefit with light movers is for HIDs and I don't see too much benefit for LEDs.
1. you got a single point of light which needs to be moved to get an even coverage. With LEDs you just spread them out instead. And get the colors arranged so that the plants get their share of each wavelength. BH seems to address this by throwing the kitchen sink at them and using warm whites that cover a very wide range.

2. You can get the HPS much closer to the plant since you won't have the heat buildup. No problemo with LEDs since they can almost touch the plant.