Yeah... that Wikipedia article isn't well written. In fact, it's wrong on many levels.
The issue of power surge doesn't make sense because once an amp's demand exceeds its power supply or caps limit, it runs out of power. Full stop.
A better explanation is found in one of the citations (prosoundweb):
"During the times when a signal is flat-topped, loudspeaker cones are not being “instructed” to move as it is receiving essentially a DC signal. This means all power goes into heating up their voice coils instead of producing sound." Any clipped signal can kill a speaker... even one which falls within the speaker's
nominal power rating.
https://www.prosoundweb.com/topics/education/why_should_we_care_about_power_amplifier_clipping/
The bottom line is that it's a waveform issue, not a power output issue.
This is a distinction that's important to capture because it explains:
1. Why crappy amps can clip even when operating within power limits, and
2. How a tweeter can be burned out, even though it may not be driven very hard by an amp fed by a clipped signal from a preamp or a source player.