Although SQLite is not designed for this type of scenario, this discussion higlights there's a strong demand for a concurrent client/server RDMS that is simple, performant and easy to deploy. PostgreSQL is powerful and feature-rich, but not simple or easy to delploy. Hence the appeal of SQLite.
For example, could SQLite power a discussion forum of moderate (or more) activity i.e. users posting comments? The Nim language forum is powered by SQLite, but activity in the forum is fairly low. [1]
Between the simplicity of SQLite and the complex, heavyweight that is PostgreSQL, there is a wide gap between these database opposites. It's a shame there is no concurrent RDMS to fill that gap.
(Note: Another poster mentions the concurrent Firebird RDMS as a possible alternative, but I haven't used it. [2])