As much as I agree with you, I think a lot of introverts would have a different take.
Silence only works like that when all the extroverts are busy yapping away. If silence becomes trendy amongst extroverts, they will create the same pressures you temporarily found relief from.
All "no" policies (no talking, no running, etc.) eventually turn into a form of bullying (see reddit if you didn't have a childhood like that). All the interesting conversations would be "shushed" as swiftly as anywhere else with a power tripping moderator.
>If silence becomes trendy amongst extroverts
That sounds like an impossibility, unless these extroverts are communicating non-verbally. How do you do the "extro-" part of extrovertedness without talking?
Non verbal communication, physical closeness to others, clothing/make-up/hair style, messages on belongings are some more ways to express extroversion
Silence can be used to assert dominance. That's why I referenced "the rules" people might be familiar with in a school setting.
Maybe I can paint a clearer picture in your head if I asked you to imagine how silence would be used during an interrogation or by the main character of an action movie?
Silence used to be a very popular choice by previous generations of extroverts and it wasn't "relaxing". It created the very same tension that compels people to make small talk (and fools of themselves) nowadays.