Yes scott22 there is plenty of evidence that a speakers ability to reproduce sounds outside the range of what you can "hear" does indeed impact the music you are able to hear. The evidence is there scientifically, from personal experience, and even just plain old common sense.
The scientific evidence is we have 4 times as many ear cells devoted to detecting frequencies above 20kHz as below. Four times. Hearing tests use sine waves that you will not hear. But your ears will detect these higher frequencies and use them to help localize and identify the source. They are there to detect transient timing information, highly important because you do not just want to know that it was a tiger that snapped the twig, you want to know where the tiger is. Real important stuff.
Perfect example, I added Townshend super tweeters to my Tekton Moabs. Even though virtually all the output is outside my hearing range they clearly improve instruments way down into the midrange and even bass. Speaking of bass, really low frequency reproduction improves a sense of space and envelopment even in recordings that don't seem to have any bass. So for example when my DBA was put on Pods I easily heard the improvement even though the first record I played had no discernible bass.
Another example, there is a sweep tone used to demagnetize that goes to 20kHz. I can't hear anywhere near 20k. But a young guy here one time was covering his ears in agony telling me to turn it down. I could hear literally nothing. Not one thing. I thought at first the super tweeters were set too high. Could easily happen since I can't hear them anyway. I was going by the way what I could hear sounded. But when we played music he was fine. So again there are huge differences between the static sine wave type test tones we use and music.
This same guy by the way, with objectively far superior hearing, couldn't hear a lot of little changes I made that were easy and obvious enough to me. So there is hearing, and there is listening, and the two sometimes overlap but not always.
By the way the function of these ear cells devoted to ultra-sonic frequencies does not degrade with age nearly as much as you would think from your rolled off hearing tests. This is another factor that explains why older more experienced listeners can continue to hear and evaluate far better than one would think based just on their rolled off hearing tests.
Finally there is common sense. You hear all kinds of things every day in the real world that involve sounds that extend far beyond your range of hearing, at least in terms of our primitive testing methods. Your speakers only really need to reproduce sounds so that they sound just like the ones you hear in real life. You. Not anyone else.
To do this properly they need to be capable of response far outside the range you might think based only on routine audiology tests.