I AM SAYING WE NEED TO MEASURE IT CORRECTLY
What is correctly... what do you propose ?
Problems with headphones vs speakers:
Speakers are heard with both ears at the same time.
Headphones have one channel per side (lets not get into the 3-4 wire discussion either)
With speakers there is also tactile feel of the body which adds to the entire 'music perception'.
Headphones lack this so just targeting the exact same EDRP is silly as the 'body input' is ignored in this case.
Speakers in rooms have room modes altering the FR in certain ways, usually more bass.
headphones can have seal issues resulting in less bass.
This means that IF we choose the same 'target' at EDRP and the speakers are not used in a 'perfect' room with 'ideal acoustics' at the right distance (between speakers and listener) and angle and headphones do not have perfect seal, pads are a bit worn or whatever what is the same EDRP character worth ?
Speaker positioning in the room and listening distance in real rooms will differ from what Klippel will tell you. Unless one measures at the exact listening spot and corrects the most obvious errors one will always use the sound of those (expensive ?) speakers in their room as reference and their headphones (with or without EQ based on whatever 'perfect' EQ they assume they are using) and the sound will still differ.
Headphone positioning and seal affects the frequency response in many cases will not be the same as was achieved with a copy of the same headphone on some 'ideal' fixture either.
Then there is the unavoidable product variance (which can be much higher than with speakers) and (silent) product changes, pad wear or replacement pads differing between the tested product and a sold copy, interaction between headphone driver and test fixture (will differ from real ears).
Let alone the substantial difference between the angle sounds enter the ear canal between speakers (in front of you from a distance) and headphones (from the sides and cm away in a 'sealed' condition) and as ears differ and HRTF differs in both cases from 'fixtures' what would a 'better' fixture add ?
Then add tonal balance issues in the recording (circle of confusion) and even the most perfect headphone/speaker might still not produce 'pleasurable' sound.
So... whatever 'error free' measurements and 'perfect fixture' and perfect matching EDRP of 'ideal speakers in ideal rooms' one can think of with 'ideal coupling' of a 'reference' headphone one can obtain there will always be errors.
So the questions would be .... What should a test fixture look like (dimensions, materials used). How to ensure proper positioning on the fixture that can be the same as on one's head. Will there be a correct 'correction' suitable (works correctly) for all IEM's, ear buds, on ear and over ear for every type of headphone design ?
I mean... driver size, type, angle, positioning on the baffle, driver-ear distance will differ.
Nah... one can scream and demand for better measurements and better corrections and better targets but the relation between measured response and perceived sound will always be lacking. There is no ideal speaker in an ideal room and no perfect coupling reference headphone to base any 'perfect standard' on.
Compromises have to be made.