I agree with everything else you said. Off axis means that the speaker doesn't point directly to the center of your head, but this is not what happens in HRTF measurements. Typically a speaker is moved around your head always pointing at the center of your head. Measurements are taken every couple of degrees.
I believe that perceived soundstage will be smaller if the headphones' frequency response matches the FR of sound coming from in front of the head closer than the FR of sound coming from left/right.
Oh interesting, that is indeed very different and also very useful. So then it would be interesting to see the FR of headphones that appear to have a good soundstage and compare them to the FR of sound coming from left/right.
Well your enclosure affects your sound a great deal. By having an open headphone, the enclosure becomes largely your surroundings. I can't say I know exactly why, but it would seem to be me if HRTF holds then perhaps open headphones have an easier time achieving the FR of a sound coming from your left/right.
If you replicate the sound signature of audio coming from afar, your brain wouldn't know the difference if it was actually quite close.
So if soundstage is affected by FR, it would lead that an EQ should affect sound stage...