I agree that PostgreSQL has some very nice extensions and if you know you are going to have multiple users (or multiple processes using it), SQLite can't compete.
But if you only have one process using the DB, then SQLite is immune to N+1 query problem since everything is in-process and there are no round-trips.
Well, yeah, but then there's stuff like enterprisedb which is postgresql + some proprietary stuff on top, and the company employs some of the postgresql core developers. So in some sense it's "PostgreSQL Enterprise Edition" in all but name.
As for mysql - I don't know why anyone wouldn't prefer mariadb - but I suppose it's conceivable mysql has features that makes it worth dealing with oracle licensing. But I doubt it.
- has strong performance vs, say, sqlite
- has "channel" and "trigger" support so you can avoid polling (which either slows down your jobs or limits your number of workers)
- is actually OSS (versus, say, mysql)