Absolutely. We've pioneered portable identity (and links and data) in a decentralised social web in Peergos: https://peergos.org/posts/decentralized-social-media
This is also pull based interestingly, but also has visibility controls being E2EE.
I don't think society needs public, or at least public by default, social media. This is even more true now in the age of LLMs and mass data harvesting.