I thought SQLite locked the entire DB when doing an INSERT. Seems like that would slow a forum app considerably. Though I guess at 1600 INSERTs per day, which averages to about 1 per minute assuming even distribution throughout the day, you won't have that many lock collisions.
The sqlite locking model can eat 1600 inserts before breakfast with only minor lock contention. The whole file lock doesn't take effect until the moment the write is ready to go to disk.
Writes were generally quite fast so the next write rarely got queued. Also we ran it single-threaded. When we moved to Postgres, that also gave us the opportunity to safely switch to phpfpm without worrying about the lock issue.
The nice thing about Postgres as opposed to SQLite is that we finally got "searching" as a feature. ;)