I still don't get it. Surely if you correct what actually arrives at the listening position, you are by definition, correcting the on and off- axis reponses.
No. You can't correct what's launched from the speaker at the listening seat.
Will a speaker+room corrected at the listening position sound better (at the listening position) if the on and off -axis responses match well? If so, why? (assuming there are 'welll behaved" corrections - eg no massive suck-outs etc)
Yes, if the on- and off-axis responses match well (assuming a fairly linear speaker to begin with), then the end result will be better. This is more or less the basis for Toole's work, which began decades ago.
The reasons are too lengthy to get into here, but you can find papers, books, videos, etc., explaining why.
Doug Schneider
www.soundstage.com