This is something poorly understood by those who eschew technical understanding. A sine wave at, say, 58 Hz (a low B-flat) is just this deep hum with almost no definition to it. Make it loud, and it's just a bigger hum that maybe reverberates in the room to become louder still. But it's still very poorly defined unless it rattles something in the room. But distort it at just 1%, and now you've added a stack of overtones to that deep sound that range up to frequencies that we hear with greater definition. I've played sine waves on the bench and can easily tell the difference between 0.002% distortion (such as produced by my HP distortion analyzer's test oscillator) and 1% (as produced by my budget-level Tektronix signal generator). Of course, sine waves are easy because they provide no masking in a test like this, but they help to illustrate the point I'm making.
When I play a tuba, the sound has a range of overtones baked into the characteristics of the instrument, and these may even be louder than that 58-Hz fundamental. Were it not so, the notes in the bottom octave of a contrabass tuba, the fundamentals of which are below 64 Hz, would be nearly unhearable. But those overtones provide two features: 1.) definition by including frequencies that are much easier to hear, and 2.) a characteristic tone that identifies the instrument and also changes with the energy being put into the sound by the performer. So, the tone very much provides cues on the intended loudness and power, which is at least as informative as the actual change in SPL. Partly, it's because the added higher harmonics are easier to hear, and partly it's because those added higher harmonics change the character of the sound which the listener interprets as the performer's intent to be more powerful. Musicians of all instruments (including singers) learn how to play at low SPL while still introducing cues of loudness, and also has to play loudly (as measured) while minimizing those changes in tone. For example, I can play a low F as a pedal tone on my bass tuba in F, such as the lowest note in the Vaughan Williams Concerto for Tuba cadenza in the first movement. But with my six-valve F tuba, I can also play it with all the valves down--no longer a pedal tone but now played on the next harmonic up but with a bugle that is now twice as long. Same note, but much different tone and character, and it simply sounds more energetic even when it isn't louder. Musicians also do this because they know their sound will be smeared by the reverberation in the hall, and they want a sound that won't get lost in that reverberation. It is not their objective to sound great up close, but to sound as they intend "out front".
So, we are trained from listening to real instruments performed by real musicians to interpret higher harmonic content as being louder or more powerful and with greater definition. It's no wonder that a playback system that adds some distortion, thus increasing the harmonic content, will sound more defined--more crisp. People whose skill is more in word choice might use a word like microdetail.
The problem, of course, is that is is less realistic--the instruments should be adding overtones and distortion based on the intentions and skill of the musician, not the playback system. Musicians would usually prefer to be in charge of that tone, and I as a listener of recorded music am more interested in what the musicians do than in what the amp designer does.
Rick "distortion can be exciting" Denney