As close to a flat response in the specific room is what it provides.
My understanding is that equalizing to flat response at the listening position is generally undesirable, and will generally result in excessive brightness. For example, the following statement is provided in the manual for the DEQX HDP-5 which I use in my system, which among many other things provides a very flexible and manually adjustable room correction function:
Room measurements typically exhibit a downward “tilt” from low bass to high treble of 6 up to 15 dB. This is caused by a number of factors including reduced dispersion and greater absorption in the room at high frequencies. Do not attempt to EQ your room measurement completely flat – that will most likely sound overly bright.
Also, when I purchased the DEQX the extremely knowledgeable dealer I purchased it from (Nyal Mellor of AcousticFrontiers.com) advised me to not mess very much with the natural high frequency rolloff of my speakers. He said that despite not having much if any knowledge of my particular speakers.
How is that unique equipment personality preserved in an always imperfect listening environment?
A factor in that may be that our hearing mechanisms give greater emphasis to first arriving sounds than to later arriving instances of the same sound. Probably not for the entire frequency spectrum, depending on the amount of delay, but at least for significant parts of it given typical in-room delays between direct vs. reflected arrival times.
Regards,
-- Al