Why do so many programs use rational databases instead of loading the data during startup and keeping it in memory? Especially for smaller datasets I would think, that a database adds unnecessary complexity and overhead. Also, a lot of data can be saved using modern RAM and when using an in-memory approach, optimized data structures can be utilised to further improve the performance
Like everyone has mentioned, because you want the data to persist across program runs. By all means, use in-memory state for truly ephemeral things like caches. You will need both for any real world task.
One more reason to use a database, even if the persisted set of data is small, is the query engine. SQLite is absolutely perfect for such small tasks. Writing SQL to query the data can save you from tons of wastefully repetitive app code.
RDBMS do not imply persisted data. There are plenty of databases which support or are designed explicitly to work as in-memory data stores. Perhaps the most popular one is SQLite, whose in-memory store is a popular choice.