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.