Use SQLite if you want a file format where you don't want to rewrite the whole file for every update, or if you're in a situation or environment where it's not feasible to have an actual database server.
Otherwise please don’t. I earn my living (amongst other things) due to organisations that went with this as blanket approach.
Use a right tool for the job. SQLite is fantastic for small to medium size datasets, shines in immutable case. Plus its maintenance and sharing cost is close to zero(something you will cherish once docker comes to play or if you want to learn or test some SQL without going through a pain of setting local permissions for your schemas).
Well, you could say the same about Postgres...
They are both databases, and the lack of scalability or (not) being able to run as a service does not change that simple (and useful) fact.