
If you have a "clipped" wave form the speaker will move out, hang for a nano-second, then come back in and hang for a nano-second, etc. When a speaker moves you want it's movement to be as smooth as possible as the speaker moves in and out. the second thing can indeed be seen as part of the first thing. There are two things you want your power amp to do, the first being adding as little distortion to the signal as is humanly possible, the second being to deliver as much "current on demand" so bass notes can be properly formed and transients will actually get through.

Heat is generally caused by distortion, distortion often caused by asking a power amp to do more than it was designed to do. The two things that kill more drivers than anything else are breakdown because of heat and plain old mechanical fatigue. You're only going to listen as loud as you listen, things like woofers and tweeters die more from accidents than from playing back music, especially todays seriously compressed music.

but you always want to overpower a speaker so you get as true a waveform as possible from the amplifier.

I have no idea how Hafler did their ratings.
