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Deviations from flat response? What do you prefer?

There is no universal "should", as the in-room response is a combined result of the speaker design, speaker placement, listening position, and your room.

Especially the bass will be heavily influenced by room and speaker placement (and listening position). Headphones are different since there's no room to mess up the result.

So if you have competent speakers, you should not EQ the response to a target, as there is a natural, correct response that automatically happens when the speakers interact with the room. Most "normal" speakers will show a slope with less energy in the top end compared to the bass. The bass level, say at 50hz (not including peaks in the response caused by the room) typically ends up somewhere around 3-10dB above the midrange/highs (2-5khz). As roughly indicated by the Harman graph you posted.
But the issue is that, specially in studio production rooms, if there is no universal target or standar then there is no proper communication between professionals. This doesn't happen with video editors and photographers, they all have monitors well calibrated for colors and contrast, and they all can see the same thing at their different studio rooms so they all can communicate and understand each other perfectly, whereas for audio such thing doesn't exist, the bass, mid or highs may sound higher or lower for every audio engineer because none of them follow the same standard in response curve.
 
But the issue is that, specially in studio production rooms, if there is no universal target or standar then there is no proper communication between professionals. This doesn't happen with video editors and photographers, they all have monitors well calibrated for colors and contrast, and they all can see the same thing at their different studio rooms so they all can communicate and understand each other perfectly, whereas for audio such thing doesn't exist, the bass, mid or highs may sound higher or lower for every audio engineer because none of them follow the same standard in response curve.

This has been discussed over hundreds of pages both here and elsewhere. You are to some extent correct, but experienced engineers are able to work around this. In addition, a lot of listening setups in studio settings are quite nearfield, and then the differences are smaller. A speaker that is anechoically flat (or close to), will have a relatively similar slope across rooms in such a situation.

Finally, in this modern day and age, you even have software that shows the overall tonality of your mix compared to averages / recommendations for the genre you are mixing, so there are many tools to help you avoid making crazy mixing/mastering choices.
 
I'm having a bit of a revelation/crisis with my speakers recently involving deviation from flat response. When I measure my big three way horns up close and try to get quasi anechoic measurements I end up eq-ing each horn/driver for flat response (fairly aggressive EQ) and then trying to align them for balance at the listening position, which typically results in a room response with a tilt of around 1 dB / octave, which I saw as a sign that it must be pretty good in terms of smooth off axis dispersion.

As a whim I decided to see how my midrange horns measured un-equalized at the listening position with the whole room response included. What they produce is a nice straight 3 dB/Octave slope that extends much higher than I expected, from 300 Hz all the way up to 7000 Hz. I decided to listen to that and after some adjustment to get the tweeter and woofer levels lining up with this rather steep slope I am amazed that it sounds good! Very relaxed, easy to listen to, and yet still full of detail and sparkle in the highs. It's very clear and easy on the ear but due to the very narrow dispersion up high it's not as immersive or present.

So I did another experiment and checked the tweeter horn un-equalized at the listening position. It also follows this same 3 dB/octave slope from about 1500 Hz up to 15000 Hz. That means I can use a broad range of crossover frequencies that produce the same straight line 3 dB/octave slope and hear how the dispersion changes the presentation. If I cross it lower I get a wider dispersion from the tweeter that then narrows when crossing over to the mid-horn. This is a bad thing, I'm told. But it doesn't sound bad in a way I expected. It still sounds natural. There's a difference in imaging effect, a more immersive sound and more vocal presence from the added dispersion at the cost of less absolute clarity, which can be seen on REW's clarity results for each driver.

So 3 dB/octave actually sounds natural in this room, at least with these big corner horn speakers. I never would have guessed it. I'm still doing some EQ for some bass peaks in the room but otherwise I'm just setting the crossovers and letting the response of each horn/driver combo do its thing unmolested, But it's such a steep slope, 24 dB down after 8 octaves! It shouldn't sound this good. It makes me think I must be missing something.

Interestingly, I saw a very steep slope like this as a target on an RTA at a night club once. You could see the signal bouncing around to the music and it was following that target closely. It sounded good, and I wasn't sure why then either. I assumed it was just because the monitoring mic. was a long ways from the speakers.
 
But the issue is that, specially in studio production rooms, if there is no universal target or standar then there is no proper communication between professionals
The idea of standardizing a "room curve" is hopelessly flawed unless you also specify detailed standards for the room (including speaker and listener location) and speaker directional characteristics. Given unknown rooms and unknown speakers, equalizing to any "standard room curve" is virtually guaranteed to screw up the sound above a few hundred Hz. Why? Because 1) the auditory system can separate the direct sound from the reflected sound to a large extent above bass frequencies, and 2) the physical hearing apparatus is not omnidirectional. What you actually perceive—especially from the midrange up—is not the sum of all sound energy that reaches an omnidirectional microphone or even a dummy head.
 
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