[mike1127]

Let's talk about balance in an ensemble with some very low instruments, some midrange instruments, and some very high instruments. Let's say the musicians play a chord with notes from the whole spectrum, and they want it to sound balanced. The musicians will play the low instruments and the high instruments in such a way that there is a lot of energy and low frequencies and at very high frequencies. The design of the instruments themselves reflects this: for instance, bass instruments are usually very large, or connected to powerful amplifiers. If you measure the energy across the spectrum, it will look something like an upside-down F-M curve.
 
The job of the microphones, recorder, etc. is to reproduce this spectral balance without changing it---therefore they need to be flat. (Exceptions in some cases: see below.)
 
Or let's talk about a studio rock recording. The mixing engineer will adjust relative balances so things sound "right"--which could mean really heavy bass or brilliant highs--or not---but it is controlled by the mixer.
 
The headphones need to be flat in order to reproduce what is on the tape. The musicians or mixing engineer is responsible for making that tape. If the style of music is bass-heavy, then the musicians or mixing engineer set that up. The headphone just reproduces it.
 
If your headphones have an inverse F-M curve they will not sound like what is on the tape.
 
The exception is: if the mixing engineer uses monitor speakers that deliberately resemble awful car speakers or iPod earbuds or whatever, then you need those awful speakers/headphones to hear what he intended. But this doesn't have anything to do with the F-M curve.

 

[mikeaj]

Yes, I agree that if the mixing engineer is striving to produce a lifelike (err...performance-like, though in reality, that depends on where you're listening from) recording, then you want your audio playback chain to be as flat as possible to reproduce the lifelike material.  This material may or may not be balanced towards equal perceived loudness in all frequencies.
 
I think in most cases, the high frequencies are actually rolled off a lot compared to an upside-down F-M curve.  The upward slope occurs around 4 kHz, and it's around the 2 kHz to 4 kHz octave that is perceived to be the loudest given the same actual loudness.  It's really the area around 10 kHz that needs to be louder to be perceived as loud.  The first harmonic of most instruments is below that, and the piccolo--and maybe flute and E-flat clarinet--is the only one that actually extends into that ear-piercing range.  Of course, the other harmonics are not as loud.  It's the bass that's relatively loud to achieve very approximately equal perceived loudness with the rest.  See here: http://www.independentrecording.net/irn/resources/freqchart/main_display.htm
 
Just taking a snapshot of a small snippet of late Romantic-era orchestral music, here is what the spectrum looks like during a chord: