I think this may irritate some, the analogy isn't perfect.
This post refers to some standard:
To learn the slightest, You have to define the other end, namely the least effcient speaker. This is all so illogical. Why is my personal experience, that the claim of "more efficient == more dynamic" is not true, overtly dismissed?! Really, I've got specimen ranging from 80dB/Watt up to...
www.audiosciencereview.com
It makes sense to understand the concept fully, literally creates sense.
A caveat besides: in Your analogy a wave is shown with ridges and valleys. You say, the valleys are filled up by random noise, hence the difference between high and low points is decreased. Wouldn't the random noise add to both, the high point and the low point? So the contrast as a difference was maintained.
Of course that can be explained. It's only to clarify.
I add to Your argument. What is the "wave" made of? Think of an identifiable package of frequencies, an acoustic event, that stands out by its "gestalt". This is pushed out into some room. It travels on a direct path to my ear, but takes many other paths also, as the sound is reflected at the room's boundaries, and repeatedly many times.
At which point in time, or after how many reflections would the "gestalt" be lost? So that it wasn't identifiable any more, transformed into noise?
Is it possible for the hearing to once catch the "gestalt" and then subsume its reflected copies under that first appearance? I think of the precedence effect here.
Can a correlation be stated between precedence (de Haas) effect and perceived dynamics?
I feel this has a lot to do with just time, namely the size of the room. I argue there is a difference between a PA system for an icehockey stadion and a stereo in a living room. Me thinks, that MTF (modulation transfer function) is a concept mostly developed for railway stations (lots of noise) and larger venues like (European?) churches (reflections, time delay).
My motivation here is, that I couldn't yet measure an MTF in my room(s) that was anything below 'excellent'.
Another fellow here measured an MTF outside in free space--a misconception?