Yes, peak power output is a bit of the sizzle and yet pretty relevant.
Music is transient and those music or sounds peaks are the road map the amplifier is following. They are instantaneous but to do it well, crystal clear and free of distortion, this is what separates low, mid or high end equipment. Head room is (or was) a term applied to a conservative rating on a well designed or well respected brand that outpaces it's own specs by these conservative ratings. In the days of selling and comparing a few years either side of 1980, Yamaha, Onkyo, Denon, Hafler, Luxman and a few other's were the brands we tested, sold, traded or ?
Sure, we looked at specs but the sound and performance wasn't summed up that way. It was in the listening environment and at many stores or specialty shops, a room or environment that could be better sounding than many homes these were sold and delivered to.
Indeed, you could see distortion rates as published for all brands or amplifiers and for many, peak power was so over-rated that you'd see specs of 5 ,8 or even 10% distortion at peak power. Other brands of audio equip tested or verified could be very forgiving. Those I mentioned and other brands were the talk of the audio purists or guru's of the days. With clean stores of dynamic headroom, this well respected equipment not only sounded better, performed better, it was also safer. It wasn't running too hot nor with higher levels of distortion, the speakers didn't have "garbage in" which is really what destroys a speaker system.
In all the years I owned and sold or traded equipment and was around some very fancy and pricy stuff, I always sided on getting good sounding efficient speakers that didn't need gobs of pricy power to make them sound nice. I always kept it simple and never turned the corner to being a 'purist' or audiophile. It had to work and be fun for me. Most audiophiles I knew were pesky, impatient, whiny and unhappy. I just think they went too far and lost the fun button.