Ok, so it seems that we actually agree that, in the 400-800Hz range, although the room may have a significant influence on the steady-state response, it is only the speaker's (anechoic) response that should be corrected.
I understood you to be arguing earlier that room correction should be implemented in the 400-800Hz range. As I understand it now, though, what you're actually saying is that only the speaker should be corrected in this range (with which I agree) - but that one way to indirectly measure the speaker is by averaging out a large number of in-room measurements.
Did I understand correctly?
Not really. Here I will be trying to demonstrate if my method of measurement is accurate enough in the 400-800Hz range. As I cannot control the room I will induce a resonance to the speaker and I will try to guess and correct that resonance based on the eventual difference between my measurements (pre and post inducing a resonance).
Assuming this will work, in the real life scenario I wouldn't know if the resonance peak is coming from the speaker or from the room as in this area both can be true: some room modes definitely still exists in the 400-800Hz range and speaker can have resonance anywhere, so it may be there as well.
Your original point (supported by @Willem) was that the resonance in this range (coming from either source, room or speaker) cannot be measured and thus effectively corrected because of short wavelength, so it doesn't make sense to apply any EQ in this range.
Let's now see how this went..
This is the initial measurement of my left speaker taken from my LP. I used MMM RTA pink noise and I took 59 samples over the horizontal area of 70cm x 40cm at my ear height. I applied 1/6 smoothing.
Then I created this filet in rePhase and introduced it into the convolution chain. As you can see the filter is applied at 650Hz, gain +2dB with Q=4. I hope we'll agree that this resonance is far from spectacular. I'm creating resonance in the speaker because I don't have knowledge nor means to modify my room to introduce such resonance, but in this frequency range it anyhow doesn't matter.
Now, my idea is to measure again and try to identify where resonance was introduced, identify it's parameters and correct it.
This is what I got when I re-measured:
Well hello precious, there you are:
Ok, let's now try to find with REW what we're dealing with here and try to correct it to put it down:
To my best knowledge I would estimate the center at 631Hz, Q at 4 and I would apply -1.5dB of correction to compensate for it.
I'd say my correction landed up pretty close to the real thing, wouldn't you agree?
If I was a construction engineer I would may have knowledge and the means to introduce similar kind of resonance to my room but I see no reason why test would end up differently. Let me once again remind you that your and @Willem 's original point was that it is practically impossible due to short wavelength to identify such resonances and even if identified and corrected it would serve no purpose as "if you move head few inches/step away it will be different".
But it turned out not to be so. Not only the resonance survived extensive averaging via MMM over the 70 x 40cm area with 1/6 smoothing applied but I was also able to identify it with pretty good accuracy and correct it. I think this proves my point.