Yeah, sure we can. :)

I have no idea what you are talking about with the CIE question.

I understand it a little bit different obviously.

Imo applying the Harman Curve to a headphone is no different than running Audyssey or Dirac on your Stereo (or surround) setup.

Of course it is a little bit different because for a stereo setup the Speakers sound different depending on the placement. A speaker in a corner will be louder than a speaker placed against only one wall. Moreso the lower frequencies are amplified more than the higher frequencies. Straightening this change in FR is a good thing and i think most people would agree that hearing the "correct" frequencies (aka "as the artist intended") is better than hearing the unadulterated "original" speaker sound.

However the part of straightening the FR is the same for headphones. ...To an extent at least.

Because then there is a reason why all the Sennheisers and Hifimans do not play back a perfectly flat curve when measured off the factory. (And neither do any Speakers that are high rated and desired by enthusiasts.)

Recording and/or mixing equipment is inherently different in itself. This is why you are wrong with the microphone analogy. Yes, you can plug a headphone into a microphone port and even record something. But a headphone is designed to to play back what a microphone is designed for- recording this playback. This means that the merits and effects of changing a recording versus changing a playback curve are not really comparable.

Let me introduce an analogy about a different kind of reproduction. I work with printers, but also when "base lining" other devices, like TVs or Projectors, that reproduce color (in contrast to sound) you are limited by the weakest link. When you want a couple of devices to produce the same colors you test which device has the smallest color range and then tune down the other devices to this base line. You can only go "so" black for example and you can not make the brighter TV go darker, you have to brighten up the darker screen.

When comparing two speakers or headphones against a "known good" and/or desired FR and sample A has a dip at let's say 4k and the desired curve has no dip there this frequency IS THERE, its just "less loud". It is played back and you CAN add it, contrary to the color analogy. I agree that, applying an EQ has some effects on the signal and there are of course physical limits with the actual driver and at some point the driver can not "go higher" and will distort the signal there is a beautyful thing in it. Because you can just stop applying the EQ at a point before distortion and effects start occuring. And at normal listening levels you can do a lot of EQ or DSPing before a human ear will be able to make out differences that are actually caused by "physical distortion of the driver"... Unless we are talking about 1$ airplane earbuds. Then maybe... ;)

You may not be able to match 100% of any given target curve every time, but you can try to get as close as possible. So why not do it?

You are right that you can not magically have an EQ add something out of thin air that wasn't there before.

But the question of OP was if you can tune suboptimal frequency curves to match a "known good" curve.

Between 20-22k Hz there are hardly any frequencies that "whatever headphone in question" ist NOT able to reproduce AT ALL. Contrary to what you say we are not in home Cinema and try to make a tweeter from a sub.

You will have dips and bumps and the EQ will tune down the bumps and push up the dips.

In regards to music the frequency range in question is much closer to 34-18/19k Hz for the most parts and most people.

Well in the traffic jam each morning during commute both cars are driving the same and you won't be faster with the Ferrari.

Well not in Germany for example. When you are a business you can buy the stuff you need to run it without paying sales taxes.

Like a carpenter who buys a hammer to make things a restaurant buys a knife to cook things.