The simple answer is that a flat frequency response system constructed with op-amps to correct the driver response will necessarily have a very un-flat phase response in the pass band. This non-flatness means component frequencies of transient sounds become unevenly delayed, resulting in a subtle transient distortion which prevents proper sound component recognition, which means fewer distinct sounds can be discerned.
Consequently, It sounds terrible. As if all the sound is coming from a fuzzy ball centred exactly between one's ears.
The HRTF issue in the answer above is only part of this - the other is that a realizable analogue domain circuit can only have a causal time response, and to correct the driver properly one needs an acausal filter.
This can be approximated digitally with a driver-matched Finite Impulse Response filter, but this requires a small time delay which is enough to make movies very jarringly out-of-sync.
And it still sounds like it's coming from inside your head, unless the HRTF is also added back in too.
So, it's not so simple after all.
To make a "transparent" system, you don't need merely a flat pass band over the human hearing range, you also need a linear phase too - a flat group delay plot - and there is some evidence to suggest that this linear phase needs to continue up to a surprisingly high frequency so that directional cues are not lost.
This is easy to verify by experiment: Open a .wav of some music you are familiar with in a sound file editor like Audacity or snd, and delete one single 44100 Hz sample from just one channel, and realign the other channel so that the first sample now happens with the second one of the edited channel, and play it back.
You will hear a very noticeable difference, even though the difference is a time delay of only 1/44100th of a second.
Consider this: sound goes about 340 mm / ms, so at 20 kHz this is a time error of plus minus one sample delay, or 50 microseconds. That's 17 mm of sound travel, yet you can hear the difference with that missing 22.67 microseconds, which is only 7.7 mm of sound travel.
The absolute cut-off of human hearing is generally regarded to be around 20 kHz, so what's happening?
The answer is that hearing tests are conducted with test tones which mostly consist of just one frequency at a time, for a fairly long time at each part of the test. But our inner ears consist of a physical structure that performs an FFT of sorts on the sound while exposing neurons to it, so that neurons at different positions correlate to different frequencies.
Individual neurons can only re-fire so fast, so in some cases a few are used one-after-the-other to keep up... but this only works up to about 4 kHz or so... Which is right where our perception of tone ends. Yet there's nothing in the brain to stop a neuron firing just any time it feels so inclined, so what's the highest frequency that matters?
The point is that the tiny phase difference between the ears is perceptible, but rather than changing how we identify sounds (by their spectrographic structure) it affects how we perceive their direction. (which the HRTF also changes!) Even though it seems like it should be "rolled off" out of our range of hearing.
The answer is that the -3dB or even -10dB point is still too low - you need to go to about the -80 dB point to get it all. And if you want to handle loud sound as well as quiet, then you need to be good down to better than -100 dB.
Which a single tone listening test is unlikely to ever see, largely because such frequencies only "count" when they arrive in phase with their other harmonics as part of a sharp transient sound - their energy in this case adds together, reaching enough of a concentration to trigger a neural response, even though as individual frequency components in isolation they may be too small to count.
Another issue is that we're constantly bombarded by many sources of ultrasonic noise anyway, probably much of it from broken neurons in our own inner ears, damaged by excessive sound level at some prior point in our lives. It would be hard to discern the isolated output tone of a listening test over such loud "local" noise!
This therefore requires "transparent" system design to use a much higher low-pass frequency so that there is space for the human low-pass to fade out (with it's own phase modulation which your brain is already "calibrated" to) before the system phase modulation starts changing the shape of transients, and shifting them around in time such that the brain can't recognise which sound they belong to any more.
With headphones it is far easier to simply construct them to have a single broadband driver with sufficient bandwidth, and rely upon the very high natural frequency response of the 'uncorrected' driver to prevent temporal distortion. This works far better with earphones, as the small mass of the driver lends itself well to this condition.
The reason for needing phase linearity is deeply rooted in the time-domain frequency-domain duality, as is the reason you can't construct a zero-delay filter that can "perfectly correct" any real physical system.
The reason it's "phase linearity" that matters and not "phase flatness" is because the overall slope of the phase curve doesn't matter - by duality, any phase slope is just equivalent to a constant time delay.
Everyone's outer ear has a different shape, and thus a different transfer function occurring at slightly different frequencies. Your brain is used to what it has, with it's own distinct resonances. If you use the wrong one, it will actually just sound worse, as the corrections your brain is used to doing will no longer correspond to the ones in the earphone's transfer function, and you will have something worse than a lack of cancellation of resonance - you'll have twice as many unbalanced poles/zeros cluttering up your phase delay, and utterly mangling your group delays and component arrive time relationships.
It will sound very unclear, and you won't be able to make out the spatial imaging encoded by the recording.
If you do a blind A/B listening test, everyone will select the uncorrected headphones which at least don't mangle the group delays so much, so that their brains can retune themselves into them.
And this is really why active headphones don't try to equalise. It's just too hard to get right.
It's also why digital room correction is the niche it is: Because using it properly requires frequent measurements, which are hard/impossible to do live, and which consumers generally don't want to know about.
Mostly because the acoustic resonances in the room under correction, which are mostly part of the bass response, keep shifting slightly as the air pressure, temperature and humidity all change, thus changing the speed of sound slightly, thus changing the resonances away from what they were when the measurement was taken.