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