IMO on-axis is of no practical usage as it is a singlle measuremetn taken strictly at axis. Move 5 deg in any direction and you will get another response.
Well, LW in even worse in that regard: it doesn't accurately describe any response you can actually get at any angle.
using single on-axis measurement to describe anything is utter nonsense.
Using LW measurement to describe anything is utter nonsense. See, I can make assertions too!
Both these statements are somewhat correct. What does make sense is using LW and On-Axis together to determine where anomalies are coming from.
This conversation did give me the idea of adding a feature to Loudspeaker Explorer where you can see all responses at all angles used for LW in a single graph. That might provide the best of both worlds: full spatial information and no averaging.