Tgb said: "what you say is true only for those supertweeters that extend down into the music range."
Earlier you've stated that a supertweeter shouldn't have any output below 15 KHz. Let's grant that for a moment just for the sake of argument: it is stipulated that we have a tweeter that cuts off very sharply right at 15 KHz.
If one can step back and think about the implications for a transition from the speaker's tweeter to the supertweeter, what you get is a completely unpredictable response.
Take a speaker with strong response from 15 KHz to 20 or above. Adding a supertweeter in this situation would give you a response that would have a significant peak in this range.
Take a speaker with more limited output in the highs (say a single full range driver design that falls rapidly above 10 KHz) and now you have a major dip in response before the supertweeter kicks in.
High frequency curves vary widely among the thousands of speakers on the market, so the above are hardly the only two examples.
So the argument essentially becomes, no matter what the characteristics of the main speaker, more is always better when it comes to high frequencies.
I find that a suspect proposition. In virtually every other aspect of audio reproduction, effort put into having well-integrated, carefully crafted matches between individual components yields better results than simply throwing a mishmash of parts together, even if each part is excellent in its own fashion.
I guess the red flag just goes up for me anytime I encounter a situation that says one product or solution is always the answer no matter what the circumstances.