Speaker power rating and amplification

This was mentioned in another thread, so I thought to help our new, inexperienced members, we could discuss it. I will start with my take on it:
Is it better to have an amplifier power rating that is higher than ones speaker power rating? Yes, it is; for best sonic performance, however, care needs to be taken. General rule of thumb: If your amp is rated higher than your speakers power rating and, you play your music at high sustained volume levels, you will damage your woofers. Why? Because at lower frequencies the current going through the coils is alternating at a slower rate, therefore, the coils experience this current for longer periods, heating them up until they get so hot that they get damaged. The tweeters on the other hand, have the current alternating at a rapid rate,
therefore, they don't experienced a sustained current as the woofers do, so they ought not to get damaged. On the other hand, if your amp is rated at a lower power rating than your speakers and, you play at high sustained volume levels your tweeters may get damaged because your amp will create distortion which destroys your tweeters; but your woofers will be okay. So if your amp is rated at a higher power rating than your speakers, use common sense and your ears. Don't play your music at very high levels for a sustained period of time.