It solves the problem of relying on 3rd party platforms to establish user identity. That is, when Alice wants to hear from Bob, they both have to be authenticated by some 3rd party Acme Corp. Alice can't know that a message is written by Bob unless she gets the message from Acme Corp. In that case she needs to trust that Acme Corp correctly vetted and authenticated the user Bob, and that their database isn't corrupted. This reliance on Acme Corp. is what has lead to walled gardens, de-platforming, bot farms, etc.

I will also add that, when done right, 3rd party platforms managing user accounts does come with benefits over Chatter Net's decentralized approach. So I consider Chatter Net an experiment to better understand the alternative.

There are some interesting features that come out of Chatter Net's approach, like the self-moderation idea discussed in other comments. I think exploring them could be rewarding.

As a final note, Chatter Net is inventing very little here. It's mainly packaging together a DID (https://www.w3.org/TR/did-core/) and Activity Pub (https://www.w3.org/TR/activitypub/) implementation into an opinionated library which is ready to deploy on existing web tech.