The warning about underpowering speakers (in the sense of definitions 2 or 3 above) goes back at least as far as the 70's, and was also related to hi fi stereo equipment, not just musical instrument equipment. Low power stereo amps were quite capable of burning up tweeters when the amps were overdriven for "party" volume.
I would still consider that over powering the tweeter. More harmonic content sends more power to the range the tweeter is working in, and the tweeter or what ever is used as a filter sees more power than it can handle.
It all comes down to understanding the limitations of the set up. People need to stop trying to do too much with too little. If they dont understand why the keep killing their equipment, it is on them to rise to that challenge of understanding. Lowering the bar with "Under powering" explanations just has people doing dumb stuff like using amplifiers rated 3-4 times higher than what their speakers can handle.