Since I agree with the core of the text (it's up to the writer), I'll focus on a small bit:

When I was a teacher, some students would hand in an entire page of writing with all their thoughts strung together by commas; not a period in sight until possibly the end. The run-on sentence is probably the worst abuse to which the comma is subjected.

Even run-on sentences are completely legitimate, depending on the effect you want. Consider for example the following:

The comma is a tool, much like a hammer. And, if one gets too opinionated about the usage of a tool, odds are the problem is not how other people use said tool. The problem is the opinionated person oneself. They should give the nearest psychologist a visit; it might be a sign of deep issues. Such as a desperate need to control the others' actions, due to failure and inability to control one's own life.

The comma is a tool, much like a hammer, and, if one gets too opinionated about the usage of a tool, odds are the problem is not how others use said tool, it's the opinionated person oneself, who should give the nearest psychologist a visit, as it might be a sign of deep issues, such as a desperate need to control the others' actions, due to failure, and inability, to control one's own life.

Both have almost the same words, and both are clearly acerbic. But look at the impact of the punctuation: while the first one sounds like carefully crafted aggression, the second one sounds like something being blurted out, at the expense of everything — including breathing. If what you want is to express yourself as if you were blurting something out, the second one is better.

So, moral of story: if you're in a position to teach people writing, it's more productive to teach what each punctuation mark does, than to simply tell when you think they should use it.