Running SQLite in production (yes, really)

I recently shipped a small Flask app, a scoring platform for a fitness competition, with SQLite as its only database. Not as a stopgap until the real database arrives: the app refuses to start with anything else, because a half-supported second database is worse than none. The conventional advice says this is a mistake. For this class of app, the conventional advice is wrong, but the deployment details will bite you if nobody warns you about them.