And that's OK. I'm sure there would still be anonymous forums, the 4chans and reddits of the world and such. But this would enable real-identity communities that we don't currently have, useful for things like public comments and discussions for local news (god, those newspaper comment sections are horrible right now), government requests for comments (like when they're starting a new development or changing land use or whatever), things like a public version of Nextdoor/Yelp/etc.
The hope is not that it would kill anonymity altogether, but that it would create some alternative communities linked to real-world identities, and maybe that would help people behave better, with real-world decorum, in those specific identities. Yeah, some people would never sign up for those... and maybe that's OK, as long as the remaining community is more civil and thoughtful?