Without this kind of acoustic filter, whatever harmonics are generated by the speaker will be heard. Even if you low-pass electronically, the harmonics generated by the speaker are still there. But the acoustic low-pass filter formed by the folds of a basshorn or the front chamber of a bandpass box attenuate them.

When also using push-pull drive, you have another level of distortion reduction. The main feature of the push-pull drive is that it cancels even harmonics. So the second harmonic is greatly reduced. That's the one of lowest frequency, closest to the passband. The next one up is the third harmonic, which is not reduced by the push-pull drive, but is 3x the frequency of the fundamentals and on the edge (or completely outside) of the passband. By the fourth harmonic, push-pull cancellation plus the depth out of band ensures practically no distortion is heard. The combination of the push-pull drive and attenuation of out-of-band harmonics make distortion very low.