BB4TB believes:
Perception is affected by the interaction of many parameters.
Most single corrective measures affect more than one parameter.
The best way to approach a given problem is to deal primarily in that problem's domain, for instance correcting room problems with room treatments.
As a result, there is an order to multiple treatments.
For instance, if a room has a 'ringing' at one or more frequencies to any significant degree, that ringing should first be reduced by room treatment. Because the room treatment for the ringing will also affect the frequency response in that room, one could apply system EQ to bring about a perception of even frequency response after installing room treatments.
If the attributes of the room are not treated, the ringing will add to the 'presence' of 'offending' frequencies. If the ringing frequencies are not electronically 'suppressed' to some degree, those frequencies will initially 'hit' at the 'correct' level and potentially build to too high a room amplitude. Additionally the subsequent decay of the offending frequencies will be prolonged. If one uses the usual types of EQ to suppress the offending frequencies to some degree, these frequencies will initially hit at 'too low' a level then build up and subsequently decay with the idea that this is more acceptable and balanced in the listener's perception. In such a case the blend of lows, mids and highs would be out of balance initially, until the ringing sets in to approximate a better balance.
In order to handle these interactive parameters with only EQ, one would need a heretofore-unknown-to-me type of EQ. An EQ that is continously 'analytical,' programmed, buffers in a 'store and release' fashion and actively adjusts - an EQ that affects each narrow frequency range such that when frequencies that will ring are detected as coming through the 'pipeline,' those frequencies will, for the first few milliseconds, be allowed to pass unsupressed in the correct ratio compared to frequencies that will not 'ring,' then suppression will be applied, increasing and then leveling off at the same rate as the ringing will build in the room and hold steady. After this, the EQ will somehow know how quickly the offending ringing frequencies should decay compared to the non-ringing frequencies and artificially suppress the ringing frequencies in the right amount and sufficiently 'early' such that in the listening environment the ringing and non-ringing frequencies will decay in their original decay ratio. And, oh yes, since each channel's speaker type and placement will provide the room with somewhat differing 'excitement,' make sure that all this frequency handling occurs independently for anywhere from 2.0 to 5.1 to X.Y channel playback.
IMHO, I think what one can do with attention to placement and $500 to $3K worth of room treatment plus potential 'normal' EQ will exceed what one could accomplish with over $10K of additional electronic alteration and no room treatment.
For those that have purist tendencies, adding room treatments in lieu of more and more electronics will also mean having the precious signal less-messed-around-with.