Amp frequency requirements for super tweeters?

I have become intrigued with discussions of the reported improvements to system sound afforded by the addition of super tweeters- specifically the air and coherence. Being in my late ‘50s, I am less concerned about the frequency extension and more concerned about how it affects what I can hear. My question is this- my amp goes to 20kHz, do I need an extended frequency range amp for driving this?
Same question for digital crossovers like the DCX2496.
Is your amp simply rated to 20k or does it actually start to roll off at 20k? If the latter, then yes, you'll likely need an amp that can handle the frequency range covered by the supertweeters. If your DAC (or source), amp and DCX all can cover up to 48k (which is what the DCX will do), then I would think from there it's only a matter of how much frequency territory the supertweeters actually cover. If they cover far in excess of 48k, then you may be leaving at least some performance gains on the table, but, if not, I'd say it would otherwise look pretty good. Hope this helps.
There's so many variables at play in a situation like this, that you really can't get a solid recommendation without a lot of effort. If this is something that you feel you need because you are trying to correct a problem in your system, they by all means, look into it. If not, then I wouldn't bother with it.
I have tried super tweeters before and they are a waste of money. If I played music and just listened to the super tweeters there was nothing there
I didn't want so say anything earlier because I have not tried them myself, but I'm not really aware of anyone who has tried them and truly likes them...
I should have also mentioned that I haven't heard them either. My first post was just a best guess and nothing more. Come to think of it, there's a pretty good chance The Cable Company may sell those type of tweeters. If they do, they'll almost certainly have a demo pair to lend out. If you're really interested, its definitely worth a call.
I bought a nice pair of super-tweeters here that play from
20KHz to 40 KHz. Came with a test tone disk. I can hear
up to the 12KHz tone, but nothing any higher. In other
words, I hear nothing coming out of the super-tweeters.
Getting older sucks. ;~(
The question is really more about the amp than the speakers.

The answer is 'yes' its useful to have bandwidth well beyond the traditional 20KHz. This is not because there is any significant information up there, its because wherever the amp has a rolloff, it will cause phase shift issues down to about 1/10th the cutoff frequency.

So if your amp rolls at 20KHz, there will be phase shift components down to about 2KHz. The ear cannot hear phase very well with individual tones, but it does use phase for image location. IOW this is easier to hear- an amp with more bandwidth will have a better soundstage. You don't need the speaker to go to 20KHz to hear this effect.
In other words, regardless of your hearing's upper limits, the high frequencies in live music have a very real effect on what is going on at the lower, more "audible" frequencies, and this goes a long way in explaining why 20KHZ shelving on "red book" CDs can sound somewhat less alive (and why LPs, with their much higher frequency range can sound so good). I find that digital with a good up-sampling DAC and a wide frequency tube amp help make the world a better place.
It's been a while, but didn't Whest come out with a component that was to help meant to address that very issue? And if so, would it make sense to go with a super tweeter, or a component like Whest makes?
How could another component open up the bandwidth of an amplifier??
"01-16-15: Atmasphere
How could another component open up the bandwidth of an amplifier??"

If I remember correctly, it was a box that went between a CD player and the preamp. Redbook specs call for the CD's highest frequency to be 20k, and then it cuts off. I believe the purpose of the component was to try and re-construct frequencies above 20k using the information that was already on the CD.

But its been a while since I read about this component. There's a good chance my details are not all correct. I'll try to find more info for you, and I'll post it.
The Whest Audio DAP.10 is the component I mentioned in my last post. Looks like its been discontinued. I'm pretty sure Stereophile reviewed it, but I couldn't it on their web site.
If the amp does not have the bandwidth, it may not matter.