I would just add that breakups in midrange drivers can result in harsh sound in the presence frequency area (upper midrange), but we think it's coming from the tweeter. Midrange driver having breakup in its top end, or tweeter breaking up in its bottom end where it meets the midrange driver is the more usual source of harshness than tweeter ringing in the very high kHz. If this occurs it is not because a tweeter is metal dome one, but because the designer used drivers beyond their safe operating area, too extended application.
Ideally you want the tweeter to start where the midrange stops, but well extended, undistorted and good sounding drivers don't come cheap, even if you build them inhouse. This is why many speakers have large FR dips and valeys where drivers meet. If this is in the presence area they may sound warm and dull.
B&W CM1 frequency response. Punchy, airy, warm, sweet and dull sounding. The crossover frequency is at 4kHz and we can see the midbass woofer is breaking up after 1.5kHz, but since the troubled area is dipping -6db, no harshness is noticable. Obviously B&W did some compromises facing the physical limitations of the driver and cabinet.