The important thing is that the amplifier should specify continuous power. Traditionally, the DIN measure was at 8 ohm and at a specified (and low) distortion level.

Today, just about any music device specifies PMPO - Peam Music Power Output - which is just a random figure how much they can charge the capacitors. It has no relation at all to true power output (continuous power rms) and to what distortion level you will get in real life. Having a power figure specified as PMPO obviously means that the amplifier will fail to produce a reasonsably distortion-free sine as soon as the capacitors are emptied and the PSU gets on its knees, begging for mercy. And besides - as already mentioned earlier - mot of the design would not have enough cooling to keep up.

In loudspeakers,not only the high-frequency elements, but also the filters, will quickly die if suffering any significant amount of power at higher frequency. I had to send two elements to get the coils rewinded after I managed a feedback loop with the vinyl player. Luckilly, the speaker manufacturer Dali did in original always custom-rewind the coils of that element so it wasn't too expensive. Multi-element speakers have a huge difference in amount of power they can handle in low and high frequencies. It can be a factor 20 or more. On the other hand, it doesn't take much power to kill our hearing at higher frequencies.