Yes, plenty of headroom is indeed, what is desirable, it keeps down distortion of transients. However all this is a lot more complex, than it appears to be. Recording studios actually use relatively little headroom, as they need to find a balance between background noise and distortion. This is actually aggravated by digital recording, which unfortunately treats audio signals in the opposite way to the way people hear. In digital recording there is a hard maximum level, which cannot be excerded. For this reason the avreage recording level is at around -12 to -14 dB below the maximum 0 dB. Exceeding this maximum level results in highly disturbing and unpleasant hard "clipping" of the signal. During the mastering process this headroom is further diminished by the use of dynamic compressors and "soft" limiters. Most pop music is released with virtually no headroom, so no transients exist. Those recordings appear to be very loud compared to uncompressed material.
Whereas with analog equipment the harmonic distortion of a signal increases with the level, this is opposite in digital recording. Although the problem of tape hiss and analog (thermal) noise is eliminated, another penomenon plagues digital recording: at very low signal levels there are not enough bits available to reproduce a signal faithfully. This means, that distortion on the low end of the dynamic range increases sharply. Lower levels mean less bits are there to resolve the signal. A resolution of 4 bits sounds rather awful !
Although bass uses up most of the available amplifier power, it also has the lowest transient content, so not much headroom is required. In addition, a bass amplifier does not need to be fast, but it must be tightly coupled to the speakers to prevent flabbyness of the sound.
Power bandwidth is the frequency response of an amplifier at full output power. It is a function of the slew rate, which is a measurement of the time it takes to produce a defined change in output voltage (the rise and fall time of the output voltage), and the higher the output power the larger is the voltage swing, and the faster the amplifier needs to be. This is the reason, why many amplifiers sound "middly" or "nasty" at high volume.
Bi-amping or tri-amping are excellent ways to achieve a high sound quality with relatively inexpensive gear. The audio quality does mainly depend on the quality of the active crossover network and its correct setup. As it is much easier to build low-powered amplifiers with a large a power-bandwidth, and only the mid/high amplifier needs to be fast. Indeed limiting the frequency response of the low-frequency ampilfier(s) helps overall performance by lowering the background noise.
All large-scale PA systems work this way, and in this case even the tweeters have their own amplifiers.
