I'm not sure why you concluded that SQLite is the problem when you built a "really cool distributed database" with Kafka. Distributed databases are complicated, Kafka's complicated.
If you're saying that a replicated Postgres setup would be simpler than what you're built, I agree; but SQLite+Litestream probably would be too.
Litestream is too much work if you're not using S3: replication over sftp. Even fossil has nicer no nonsense replication done over http/s. It's way easier to set up mysql with replication than manage unix accounts and public keys.
If you're saying that a replicated Postgres setup would be simpler than what you're built, I agree; but SQLite+Litestream probably would be too.