Basecamp HQ has a policy like that, 'library day'.
Just a guess: some extroverts find "library day" just as unpleasant as others find non-library days?
I really like the way Amtrak handles this: At least on the Northeast Corridor, most of their trains have a "quiet car". Whether or not you sit in it is optional.
extroverts work at the office
introverts work from home.