I disagree.
First of all, I don't see a real life situation where someone would insist on using the same amount of power for all his headphones. We all use differing amplification for different headphones, its common sense! Provided you use enough force (amplification) , both light and heavy diaphragms would move in accordance with the signal applied.
The actual benefit of a thinner diaphragm is not that it can be put to motion easily but rather that it can be stopped much more easily. A headphone diaphragm is like a mass loaded spring which continues to oscillate much longer after the signal was applied and needs an external force (damping material) to stop when it should.
With a thinner diaphragm, we need a much lighter damping material compared to what we would need for a thicker diaphragm. So, with a thinner diaphragm we avoid the side effects of damping materials (which all of them have to some degree) and we have a headphone which sounds much more open as the more heavily damped headphones tend to sound rather closed in. 

I'm looking at it from a measurement standpoint, too.

If you send a sine wave signal to an amplifier with voltage gain and voltage output (so no funny Bakoon current-output business), the signal that the headphone should receive will be a sine wave at the same voltage amplitude but with different frequencies.

With orthodynamic headphones, this essentially means you have the same power across the entire frequency spectrum. It's just a matter of "how fast" that power is being delivered.

Let's look at it from a different point of view: if I have two headphones, same impedance rating, orthodynamic (so no impedance swing), magnetic field gradients the same, etc... but one has a thinner diaphragm than the other, what would happen when I send the same signal to either one?

They both receive the same current, in the same magnetic field, so force applied to both is the same. But obviously the acceleration applied to both will be different. The thinner diaphragm, which is lighter, will get more acceleration, so... technically, more "stopping power" mechanically. At higher frequencies, this means that the diaphragm will be forced to stop when it has not gone very far. However, at lower frequencies, the diaphragm will go further before it is forced to stop. During this time that the diaphragm takes to travel this "further distance" it technically is also experiencing air resistance. With the same surface area, air resistance should be the same for both, but the thinner diaphragm will once again experience more acceleration due to air resistance. More acceleration = more stopping force.

Now, a good amplifier will apply a force and then stop applying that force, right? So after that initial acceleration, the only force that the diaphragm would experience is air resistance here. So no matter how strong the original acceleration was, the diaphragm will always experience this air resistance, and so it will always stop a bit short of where it should end up being. This may not matter much at higher frequencies where starting and stopping forces are applied more rapidly, but at lower frequencies, sometimes, the diaphragm may actually stop even before the stopping force is applied. We are talking big surface area with barely any mass here.

In practice, I think this is why electrostats always measure with very mediocre low bass performance. I mean... don't take it from me. Take it from those measurements. For instance, let's look at ultra's measurements of the SR-009:
http://www.changstar.com/index.php/topic,23.msg32768.html#msg32768

I'm seeing bass drop off below 60Hz. This may be due to poor fit, but I don't think so. It is very likely that air is acting like an acoustic dampener here, and it's forcing the e-stat diaphragm to stop before it reaches maximum excursion.

Also by that logic, a good seal would mean less air between ear and diaphragm, which means... technically less air resistance. What would happen? Bass should increase.

So that's why I believe air resistance is significant here. But of course, you may very well be right that it doesn't matter.

As for open-ness and such, I think we'll have a discussion on that soon.

I think you're missing air resistance there.

My hypothesis is that because the diaphragm gets thinner but its surface area remains the same, the effect of air resistance becomes more pronounced, and at lower frequencies, specifically, where the start/stop forces may not be enough to overcome this air resistance, the diaphragm won't move as far as it could.

So this "braking" happens due to natural air resistance, and not because of any electrical property. From an electrical standpoint, the conducting traces (and the cable) are the only things that should matter, so the amplifier won't necessarily see and be able to account for this mechanical incidence.

Conversely, for e-stats, the capacitance will create a reactance at lower frequencies, which alters how much power is being delivered, but I don't think the amp is doing anything special to account for this air resistance.

This can easily be remedied by increasing the "force" as frequency gets lower (do a bass boost), right? But even when you do that, e-stats can't sustain the same bass body and impact as orthodynamic/planar magnetic headphones. So something else is at work here. This is just my theory on it.

A headphone is more than just an electrical device after all.

Don't you think that some of you guys are being a bit dismissive of the push by engineers for ever thinner and lighter diaphragms? Wasn't that what Stax and other current manufacturers like Audeze and Hifiman have been evolving toward since the Omega/007/009 and LCD3/HE1000?

Not necessarily dissing thinner and lighter diaphragms. They proly bring some goodness to them. Just not following the air resistance, amplifier and "speed" explanation.

Also, not sure if this applies to every type of driver, but I was under the impression that for low frequency reproduction one needs a little bit of mass, and for high frequencies low mass, so there might be sweet spot.  Therefore I honestly don't know for sure what is the deal with having super thin diaphragms as a cure all, and the thinner the better.

What I can say though is that I believe the LCD-X and the Stax cans seem to have fairly thin diaphragms. And those require seal to keep pressure under control or bass is gone bye-bye. On the other hand, there might be some distortion benefits since it appears that both LCD-X and Stax cans have low distortion numbers across the audible frequency range.

An-off-my-butt theory about that could be that the low mass takes care of the distortion and performance on the higher frequencies, while the required seal takes care of the distortion at the lower frequencies. There might be a sweet spoot about the thinness here as well. Perhaps too much and there may not be enough mass to drive low frequencies inside the sealed volume. This kind of falls into place with my understanding of the importance of acousitc impedance and limited knowledge about drivers, so it's easier to digest for me than the air resistance talk. That does not necesarily make me right, and I'm not about to spread the word about things I'm not an expert on.