At their core these drivers are all relatively similar. What Chu was talking about are electrostatics in general but the Stax drivers are all mostly the same affair. Move over to what Beyer, Sennheiser, Jecklin or Koss were doing and you'll see some very different designs. Sony probably has the oddest one of them all if the literature is to be believed.
Like I say below, it's not really a matter of dishing out more energy for a flat response but rather the amp being able to sustain full voltage swing into the given load. The huge voltage swing of the BHSE and T2 are naturally a factor here since at normal levels the amps are just idling.
Indeed on the electrical side of things, I have no idea the different the load is to the amplifier. However, on the mechanical side, stax specifically refers to increase in "ease of displacement" of the membrane by using a thinner diaphragm (with less inertia). With the o2, isn't the issue of uncontrolled bass at least partly due to the lack of control of this membrane inertia unless the amplifier has sufficient drive capability? At least, this is how it works with traditional electro-dynamic speakers. The membrane mass in electrostatic transducer is much lower and the stiffness very high by it's still got some elasticity and inertia.
Then, in regards to the less is more, indeed I have no idea how different the 727 is from say a KGSS (not so different then?). But the point was also about the power: in an electro-dynamic amp, the first watt matters much more than the 300 Watts of reserve given this is 90% of the typical recording (unless you're listening to overly compressed crap recordings eh ;) ).
Let's start off with one thing, the diaphragm doesn't move and it certainly doesn't flab around as it is tight as a drum. The sound is produced by vibrating the very taught diaphragm. If the diaphragm would move at all then the ultra low distortion figures would quickly disappear and be replaced by horn levels. What we have is a reactive driver which is essentially a capacitor so any similarities to resistance based drivers have no bearing here. While amps like the BHSE and T2 are massively over spec for the job at hand it is nothing like driving a headphone from a 300W amp.
First thing to look into is Ohm's law and how that translates into impedance vs. current vs. voltage. A planar magnetic driver has very little change to its impedance depending on frequency, dynamic drivers can vary quite a bit but electrostatics have a gigantic impedance swing. To maintain the same output voltage into any given load then you need current, in fact a constant current supply. The old way of using a resistor for this is inadequate and an inductor makes less than no sense. The "tube sound" people often talk about is due to how the tubes are driven and plate resistors certainly are a part of that. Take the SRM-007t, replace the tubes with 6S4A's, add a CCS for the output and a nice PSU and it is a damn good amp, none of that warm tube sound. Let's say you are listening at any given volume (i.e. voltage level) and the amp is asked to reproduce some bass note but it lacks current to swing the full voltage into the given load. What happens is that the amp doesn't have full grip on the diaphragm so the bass appears to be loose.
There are naturally other factors to consider (slew rate, output impedance, psu design etc.) but this will do. Now the improvement isn't just linked to the bass but the entire spectrum but most people seem to focus on the bass. I for one value a lot more the benefits more power brings to the soundstage. The goal of any good amp is to supply the transducer with enough power so it can do its own thing. Sadly this is often very, very expensive and leads to insanely complex amps like the SRM-T2 (though at its core it is very simple).
As for the 727, it is rather different from the KGSS. It's more like a spruced up 323 but with the feedback loop cut tragically short. Not a bad amp once that is fixed but as with most of the Stax amps, there are certainly ways to do it better. It does improve on the KGSS by being fully CCS loaded (i.e. what the KGSSHV does for the KGSS plus extra voltage) but in practice the KGSS is a better amp to these ears.