It's not about the actual numbers, it's about ensuring the amp will have enough headroom for peaks in the music and overall playback that the performance will be linear with a particular headphones. A lot of amps may be able to output, say, 4W, but may only be in Class A mode for part of their power output. Also, prior to planar headphones becoming popular, amps were more often designed for high-impedance, high sensitive headphones and they didn't do a good job with planar headphones at all. So putting an arbitrary figure out there was an easy way to deal with this. The numbers wont tell you how well an amp will perform though, not by a long shot.
That's partially true, yes. That's why whenever people do power calculations, they usually determine the power needed to reach > 110 dB SPL because that will determine the power needed to reach a peak in the music. Even at 110 dB SPL, that's quite a large number and I would probably be surprised if my music ever reached that level, even if I'm on a public bus. As calculated earlier, the LCD-2.2 only needs ~700 mW of power to reach a peak of ~117 dB SPL.
While on the topic of planar magnetic headphones and power needed though, the LCD-X is far more sensitive than the LCD-2.2 and it's at a much lower impedance (Tyll measured 0.28 mW to reach 90 dB SPL at a 15 Ω impedance). Audeze still suggests having 1-4 W of power to drive them, which is utterly insane. I rarely had to ever turn the potentiometer past the 11 o'clock position on the Objective 2 at 1.0x gain to get sufficiently loud volume levels, and the O2 definitely has less than 1 W of power output. Intuitively, it doesn't make sense to get the Geek 1000 for the LCD-2.2, or the Geek 750 for the LCD-X (it only takes 227 mW to reach 119 dB SPL).
So that brings me back to the question if the Geek 1000 really has any benefits. Again, we only know one VRMS value at one impedance value, so we really have no information about it otherwise. If talking about planar magnetic headphones, current is usually more important than voltage, and as of right now we have no information about the Geek 1000's current output versus that of the Geek 450. Power linearity is something to keep in mind too, yes, but there seems to be very little data about that topic.
"Need" is definitely a tricky one. I listen to music using a 1W SET amp. Yet its performance is very linear within that 1W. I've had amps here that could output 4W that don't even remotely deliver what that amp can. Even if an amp can get loud enough, the real test is to play fast, complex music at higher volumes and listen to hear if the soundstage collapses. That is something the numbers cannot tell you. That's entirely dependant on the design, so I don't think it's insane for Audeze to write that the "Optimal Power Requirement" is an amp with 1-4W given the wide variation in amp designs out there.
Since this is about the Geek Out 1000 (which is on its way to me) I am very curious to find out how well it does from a USB port. I suspect that, like other people, I should have got the lowest power version as I'm using IEMs more often these days, and if the volume control is a dangerous issue, then it may turn out the unit is somewhat useless to me.