John Dunlavy also said this,
Dunlavy: That's right. You can go one way but not the other. Flat
on-axis response provides very poor correlation, in general, with what
you hear. On the other hand, if you have near-perfect impulse and step
responses, it follows that you must also then have from that a
near-perfect frequency response on-axis. And using a first-order
crossover network is the only way you can achieve accurate impulse and
step responses. As soon as you go to a second-order crossover, the
impulse response is hideous.
And as Toole proved when at Harman, a flat on-axis response was absolutely critical to how well a speaker will be considered to sound.