But this is the argument that says reproducing inaudible frequencies can actually reduce audible quality.
Since the inaudible frequencies are inaudible - they can't improve the sound. But they can inter-modulate with other frequencies (especially in the output transducer) to create audible distortion that otherwise wouldn't exist.
I'm afraid that such IM distortion is part of how a rimshot, for instance (or a glockenspiel hit, some other stuff) sounds, where the IM comes from the air transmission. So is it distortion or signal properties? I think that's a semantic issue that is going to be very hard to settle.