Electrostatic headphones and speakers have the least distortion when they have a constant charge on the diaphragm. This was established at least as far back as PJ Walker who designed the original Quad electrostatic speaker.
The "rationale" for having a "large" capacitor in the bias supply, e.g. 1 uf or more, is to smooth out any residual AC so the diaphragm charge and voltage remain constant. However, once the diaphragm is charged, the amount of current needed to maintain the charge is minuscule, so that in fact even a "small" capacitor (Stax uses 0.1 uf) is more than sufficient. This is illustrated by the fact that if you use an old Stax converter box, which contains a step-up transformer and bias supply but no active electronics, charge up the headphones and then disconnect the bias supply from AC, the headphones will continue to play for some time. The large value safety resistor used by Stax (about 5 megohms) between the last bias capacitor and the diaphragm ensure that any current traveling to the diaphragm is very low so the diaphragm cannot get zapped. Companies like iFi and Woo that don't follow these design parameters either don't understand or ignore these facts. iFi Audio's use of a high voltage battery to "power" the bias supply is, IMHO, an expensive solution in search of a non-existent problem.