>Wikipedia is another example [of the public square]
Quite the opposite; Wikipedia is explicitly based on published reliable sources. They have a specific rule[1] excluding information that was not published in such way.
There are certain advantages to this rule, and its utility has been validated through Wikipedia's long, and ongoing, run. Nonetheless this cathedral mindset cannot be compared to a public square in any way other than being a very opposite.
In particular the published reliable sources rule excludes general blogs and public forums and the likes, thus excluding the majority of discourse & voices on the internet. Even expert sources, if self-published, can only be used in limited way and with caution.
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[1] "If no reliable sources can be found on a topic, Wikipedia should not have an article on it", https://en.wikipedia.org/wiki/Wikipedia:Reliable_sources