power output has everything to do with it. You cant run a 22 watt rms stereo to power 125 watt rms speakers
I will have to disagree, to a point.... since I've been doing installs longer than I wish to admit, you don't have to run a speaker to it's limits to have great sound. Albeit, you will maximize volume... what you lose with less power is actually control of the motor structure of the speaker. Speaker size is what really has to be realized here, yes you can't run a huge subwoofer with a tiny amp, but a speaker will work fine if under powered as long as not driven into distortion.
Here's one for ya... in my competition truck, I was running 500 watts RMS off some old school, long time not made, MTX thunder amps to a set of 5 1/4" components in my kick panels. Sooooo.... why didn't I blow them??? I'll tell ya why, because power output doesn't mean as much when you're running in the upper wavelengths and when cross-over properly.
Some of my resume.... Audiocontrol install school, MTX install school and as well as Rockford install school. I was a box designer and installer, that also worked the floor..... in the 90's when audio was huge.