The reason to have a more powerful amplifier is not to play the music louder, but to play the music more accurately. The soundstage "opens up" because the peaks can get louder while the valleys stay quieter. The music also sounds more real because, again, the peaks can get louder. The reserve headroom in the amplifier makes all the difference. The sharp, high peak of a whip crack or even just a smack can require near infinite power to duplicate.
My viewpoint is that playing the music either louder or quieter than the original session is a type of distortion- at least that's what I tell my wife when she wants me to turn it down.