By adding a vibration wave to create a small dithered motion, the mass frees itself of static friction or "stiction" so that it can move freely with only low-level dynamic friction.
Current causes force which equals acceleration (F=ma) and not position changes which are a 2nd integral of acceleration or 12dB/octave reduced amplitude with frequency. This is just enough to overcome slack in the mechanics and prevents stiction from slowing the response.
Linear superposition applies so its position would only go back & forth when idle, before a valve position-change command. The wave then just modulates the acceleration and braking to the next position with vibration so it doesn't really do what you suggested.
HDD's do the same thing before spinning up the disk by dithering the magnetic voice coil to rotary head-arm assembly. This is so the R/W heads don't stick to the disk and rip off from high acceleration to near 50~100 KPH in a few seconds. It might sound like a rising buzz-sweep, then click to unlock and then it starts spin-up.