Does treble response beyond my hearing matter?

Been thinking about getting my hearing checked. Used to get it checked annually when I was in the Air Force, but that been a couple of decades ago.

Thinking about making some changes in my system so when looking at speakers, does treble response beyond my hearing matter?
If I am interpreting accurately what you mean, frequency response matters beyond the range of human hearing. Amplification with a wide frequency response is generally accepted to mean a greater linearity (sound quality) in sound reproduction. Most audio gear extends fr beyound the range of human hearing so that what you do hear sounds better.
Yes, first you buy an amplifier with super-wide bandwidth and then buy Transparent cables to limit the bandwidth.
IMO, the way you are approaching this is putting you straight on the road to audio hell. Everyone does the same thing - they buy products that are "revealing", "detailed", "heard things I never heard before", supertweeters your dog can hear, etc. Then they come on to A'gon and bitch how their systems are bright and harsh.

Just listen to some speakers and buy what sounds good. Don't worry about the specs. All of the speakers you could reasonably buy go out as high as you need them to go. If you can't trust your own ears, then find someone whose ears you do trust and let him pick the speakers for you.
On the grand scale of things, no.
Mapman, why? Even if I can't hear above a certain frequency, in the range that I do hear, wouldn't having a higher treble response add to "air" or sparkle? I think that is what Arnettpartnetrs was alluding to, or at least in part.

I'll certainly listen to speakers, but some that I am considering are ID. Some have great shipping/return policies while other are just fair so I'm looking for ways to reasonably narrow the field.
I wish I could find the link, but I was reading something the other day on hi resolution audio and it talked about why Redbook CD is more than adequate to exceed the human capacity for hearing. The interesting thing was that the high res media could include things behind the range of human hearing but in some systems it could actually cause distortion in the audible range. It seems that higher could do nothing if you can't hear it, but could add distortion within the audible range under some circumstances.

Don't worry about what you can't hear, just judge based on what you can.

If the specs look good up to the limit of your hearing, you are probably in pretty good shape, no matter what might be measured beyond.

When I was young, I could hear test tones up to 20khz. Now, at 54, only up to about 12-14 or so. That's typical of how our ears age.

It can be a good thing though. By design, not much music occurs in the upper ranges of human hearing, but a lot of noise and distortions can. So not being able to hear up there can be a blessing. I find most music a lot less fatiguing these days than I did in my youth.
" I find most music a lot less fatiguing these days than I did in my youth."

Well, in my youth I listened to most things too loud and I often added more highs/lows. I used to think I needed to listen to rock music at concert levels. Now I realize that concert audio usually isn't very good and often is far too loud. Earplugs should not be necessary, for instance.

In the case of acoustic music it's better to listen at realistic volumes. That means the classical guitar or lute, for instance, should be dialed back until it's no louder than the real thing.
There has, a few years back, serious research been done - sadly do not remember where- which suggests that you do "feel" in music playback if information above 15 kcycles is missing.

While everyone is certainly entitled to their own opinions, FWIW, here's mine.

Although the original question does provoke different thoughts, I don't think it is relevant to the actual sound a speaker will produce. It is possible for a speaker with a somewhat limited frequency extension to have an unpleasant treble, and one with much more extension to sound very pleasing or vise versa. It is much more important to consider synergy of the system's components and cables with the speakers.

Having experience with various models of JMR speakers, I found that two, having the same specification for treble response sounded quite different in regard to "air or sparkle" with exactly the same components and cables. Trying different speaker cables proved that one speaker seemed to be affected more than the other, and could sound quite good with the right cable.

When looking at a speaker's specifications, I think sensitivity and impedance characteristics are much more important, so that you match a suitable amp. This assures peak performance, then use other components and cables for good synergy.
I'm looking for ways to reasonably narrow the field.
Of course, taken "with a grain of salt", reading multiple consistent reviews, and seeing the same comments on this forum about a speaker makes more sense than looking at a frequency specification, IMHO.