Is this sentence punctuated correctly?

I think your ear is telling you subliminally that the wording is awkward. What punctuation marks are going to improve this regardless of where you stick em?

Yes, that is correct. “The quieter you become” is essentially a conditional clause; it’s another way of saying “if you become quieter”. Rewording a sentence can help clarify. “If you become quieter, you can hear more” is correctly punctuated, so this sentence, which says the same thing, is as well.

We put commas after conditions. So if you flip the sentence, “You hear more the more you become quieter”, awkward use of “more” or not, here, there would be no comma since the condition comes second.

Yes.

The more we see and hear grammatical errors, the harder it is to recognize what’s correct. “Sounds right” is a useless standard.

Television is probably a major contributor to the viral spread of errors and weird expressions that seem to crop up suddenly and take hold, and then it’s the correct construction that sounds funny to people. And I’m sure the internet is not supporting better English. Present case excepted, of course.