Frequency response + or - 1 dB ??

A powerful DSP unit can probably get you pretty close at the microphone location, but to do it right, you'd need to exclude reflections.

When I first had access to good test equipment, as an enthusiastic amateur, I built a speaker that was about +/- 1.25 dB over most of the spectrum (room size limited how low I could get good data).  I remember vividly tweaking the crossover to get closer and closer to "flat", and that as I did so, the speaker sounded worse and worse!   I persevered, having faith that everything would sound right when I finally got to the promised land.   Well, it didn't happen.  When I was done, it was a truly dreadful sounding speaker. 

I won't bore you with my quest for understanding that experience and where it led me, but let's just say that "flat" would not be my goal for a high-end home audio loudspeaker. 

@erik_squires makes an interesting observation:  "...in the room it all goes to hell."

In my opinion there are really TWO frequency responses that a designer needs to get "right":  The frequency response of the first-arrival sound, and the frequency response of the reflections.  By way of example, live unamplified instruments get both of these "right", and the result sounds pretty good.   

Duke

Well, it didn't happen. When I was done, it was a truly dreadful sounding speaker.

"It was probably not measured properly and not really flat. Why else would it sound dreadful?"

Actually, you are right! I was only measuring the on-axis response, and ignoring the off-axis response, because back then I didn’t know any better!

But here is another critical piece of the puzzle: "Flat" sounds "thin and bright" to most people.

And a gently downward-sloping curve sounds "flat" to most people.

There’s an excellent discussion of the subject in this review of the Dutch & Dutch 8c loudspeaker, scroll down about 1/4 of the way:

https://audiophilestyle.com/ca/reviews/dutch-dutch-8c-loudspeaker-review-r739/

The author draws on an extensive controlled blind study conducted by Sean Olive and Floyd Toole, and says,

"Most participants in the study preferred a frequency response from 20 Hz with a straight line to -10 dB at 20 kHz. A measured “flat” in-room frequency response is not the preferred target, as it sounds too thin or lacking bass."

If I was designing a studio monitor the goal posts would be in a different place, and "flat" measured response might very well make sense, depending on what type of monitor it was (tracking, mixing, or mastering).

Duke