There is no cure for the time-domain performance characteristics of a driver;
I’ve seen good evidence that notch filters not only can damp the ringing, but also reduce overall tweeter distortion. Having said this, I’ve never purchased a tweeter with significant ringing, so I can’t argue the point much with first hand information. See if you can find the old threads at DIYaudio on this.
A similar argument is made in rooms, something about linear phase systems can be damped by reducing the input. In any event, I won’t argue this point, but thought it was interesting.
What I can say is that there’s a lot of metal dome speakers out there with measurable ringing in a lot of reviews and living rooms. While personally I prefer to have tweeters with little to no stored energy, lots of people have no problem with them at all. They may even give the listener a euphonic sense of air.Â