A couple things. Put simply, a choke is an inductor and an electrostatic headphone looks kind of like a capacitor. Look in any electronics textbook and you will see that when you connect an inductor with a capacitor you get a resonant circuit, which means you can have a peak in the frequency response at the resonance frequency.
I said the headphone looks “kind of” like a capacitor. It doesn’t exactly resemble a capacitor because it makes sound, which means it uses power. The power spectrum of music is highest in the mid-bass to lower mid-range areas (approximately 50-300 Hz). The impedance of a choke rises with frequency, which means that it requires more current to drive it at low frequencies, exactly where the headphone is requiring the most current and voltage to make music. This increases the distortion of the output device.
The largest commercial plate choke I have found runs around 200H. This has an impedance around 25 kilohms at 20 Hz, rising linearly with frequency from there so at 40 Hz its impedance is 50 kHz, which is a typical resistance for a stat amp plate resistor. So at the lowest bass frequencies it requires/diverts more current from the headphone than a typical plate resistor.
This is all based on an ideal choke, ignoring the possible resonances and other imperfections of a real world device.
With a resistor load, you don't have the possibility of a peak in the frequency response but the resistor requires curent to drive it through the whole frequency spectrum. In fact, with a resistor load, the amplifier actually wastes more current (and power) driving the resistor than driving the headphone.
By comparison a really good current source load demands a negligible amount of current, which means all the standing current of the output device is available to drive the headphones, which is what you want. As I said elsewhere, it converts an amp for driving output resistors to an amp for driving headphones. It is simply a better technology. This is why Stax has used current source loads in its solid state amps in place of resistor loads since the 1970s.