Originally Posted by DavidK442
Is the general thought that using equalization to "color" the direct output of the speaker (250hz and up) in an attempt to flatten the total in-room response (direct + reflected) beneficial or detrimental?
Can't speak for "general thought", but I definitely consider equalization above Schroder useful IF done effectively. When you say "flatten" the response, I'm not sure whether you mean attempting to remove peaks & dips in the higher frequencies or aiming for a target curve that is a horizontal straight line, but both are bad ideas.
It is pointless to pursue equalizing away individual peaks & dips in the higher frequencies because of how small the wavelengths are. Move your head an inch or two and you're out of the correction zone. Even worse, the corrective filters are no longer lining up with the problems they were intended to correct, so it's actually making the frequency response worse.
Since our human hearing isn't flat across the audible frequency range, a measured flat target curve will sound thin (too little bass, too much treble) to most listeners. It will also remove naturally occuring room gain which our ears have come to expect. When looking to design a default target curve, Lyngdorf did research on what listeners considered "natural" sound and discovered that flattening room gain away wasn't a good idea.
What is useful in the higher frequencies is equalization that behaves like a gentle tone control to bring the overall frequency response in line. Most surround set-ups are comprised of non-identical speakers, and even when identical speakers are use all around, they're in different locations around the room. This means that tonality will be different from speaker to speaker. If you can use equalization to timbre match the speakers (make the response similar, not flat) then sounds won't change character as they move around the room. It's worth colouring the direct sound of speakers to achieve that result, considering we were never going to hear the direct sound by itself anyway.
Originally Posted by DavidK442
Would be great if someone could link to an actual blind A/B comparison.
The only recent one I've seen was Sean Olive's room correction comparison
from 2009. Like all tests that Harman does, this one was based on listener preference; i.e., tests subjects were asked which one they liked the most, not which one sounded most "accurate" (whatever that would mean anyway).
At this point, his comparison is no longer useful for guaging actual products since almost all the room correction technologies in that comparison have made significant changes over the intervening years. However, the two main conclusions from that research paper remain valid: a) the smoother the response (fewer/smaller peaks & dips), the more it was preferred; and b) a response that was perceived flat was preferred to a response that measured flat.
So, to your original question: rather than "flatten" the response, better to smoothen it out and tilt it to sound natural.