You can NOT just ignore power ratings on a speaker.
I'm not so sure, after all, how are the numbers arrived at?
For example, the maximum wattage, would exceeding it put the drivers past their mechanical excursion limits? Woofer, midrange and tweeter drivers will have different limits, so then the spectra of the signal used would be useful to know. But that information is not provided.
Or is the max wattage the thermal limit? There again, each driver will have a different limit, and time then becomes a factor; if 100 watts of pink noise for 500 ms will melt the voice coils, how much music would it take? After all, the temporal and spectral makeup of music is very different than pink noise, and is even different between styles of music.
I completely agree that a speaker's power handling should
not be thought of as irrelevant, but there are more details that need to be known, and the "25 - 120 watts" rating that is usually provided is not enough.
The minimum rating of a speaker is to show how efficient a speaker is meaning even a lwo watt amp will power the speaker to an enjoyable listening level.
Doesn't the sensitivity rating provide a better metric for that?
A speaker can certainly be damaged by an underpowered amp. A speaker will blow when an amp goes into clipping. Pushing a low powered amp to volumes the amp is not capable of getting to without adding distortion will clip an amp.
Absolutely! But clipping 1dB off the peaks won't hurt anything, the clipping must produce enough energy to do damage. For example, a seven watt SET amplifier driven into extreme clipping will produce fourteen watts, that's not enough power to damage a tweeter that can take twenty, much less a woofer or midrange.