Punctuation is notation for the music of speech.
The written words themselves convey the sounds, but the punctuation gives you emphasis and rhythm. Speech that is monotone may engage the linguistic areas of the brain, but effective writing and artful writing engages much more: it engages the emotions and triggers memories and the imagination. It is a whole-brain experience.
I realized at some point (I suppose when I started reading to my son before he could read for himself) that I read silently even more slowly than I read aloud, which seems remarkable because silent reading is far less encumbered by the mechanics of spoken language. Most people, of course, read much more quickly when doing so silently.
My eyes and mind still move at a very high speed when reading silently, but there are many loops and backtracking and retracing. My mind rolls the words around in my head; I re-read some significant percentage of words and sentences. Occasionally I will re-read particular sentences or phrases many times, and go off on tangents related to the idea or way of expressing it.
For me, the experience of the art of the written word–participating in that as a reader–is as big a part of the experience as gleaning the literal meaning the writer is trying to communicate.
This means that in my lifetime of reading, I will only have read a fraction of what I would have read if I read faster. I am certainly not saying it is better, per se.
What I am saying is that when you are editing your own writing, if you read what you have written out loud, instead of just silently, and make a sincere effort to decode it as a reader would decode it–pause for the commas and don’t pause where there are none, and so on–I believe this might provide some insight for you into how to improve the music of your writing in the ears of your readers.