The main reason lightness matters is because it gives an electrostatic diaphragm zero resistance to motion, so the sound happens exactly when the amplifier signal happens. A conventional loudspeaker's diaphragm's weight causes a delay before it gets moving, and this includes planar magnetics that have metal deposited on a relatively thick membrane or are made entirely of metal. And worse, the delay depends on frequency, so transients, musical notes, and harmonics don't quite line up in time.
More than just diaphragm heaviness, regular speakers have other drawbacks, too. For instance, cones are vibrated from the middle, domes from the edge, etc., but they're not perfectly stiff, so they flex instead of moving as one. Above a certain frequency, they even start adding and subtracting sounds as a result of breaking up into small, individually vibrating areas.
An electrostatic's diaphragm, however, can't possibly break up, because it's pushed and pulled evenly over its entire area. This leaves the sound just as it was recorded.
Next, an electrostatic is very simple and elegant, unlike a regular speaker's complex set of interacting parts that never quite balance out -- voice coil, magnet, diaphragm, surround, spider, basket, magnetic field circuit, pole plate, pole vent, dust cap, and pigtails.
An electrostatic is just a thin membrane, thinner than plastic wrap, stretched between two conductive screens. Because of this, an electrostatic diaphragm's motion comes as close as possible to perfectly following the signal. In other words, you get the least possible distortion.
Lastly, a JansZen's electrostatic diaphragms are ideally "damped," so they not only get going instantly, but also stop instantly. This is what makes their transients so realistic.