SQLite was originally started as a local database library for use during development for times when the main networked database was not available. It used dbm as the underlying storage mechanism, with the dbm API roughly being string keys with string values. ie all underlying values were actually stored as strings. The SQLite code would automatically do conversions - eg the plus operator would convert the strings to int or float, add them, and generate a stringified number as a result. The vast majority of implementation code did not have to care about types, and very local decisions could be made such as in the addition example.
TCL was used as a dev wrapper language at the time, and it functioned the same way.
It was only in mid-2004 that SQLite 3 was released which used its own storage backend, and that allowed for the 5 supported storage types (int64, string, bytes, float, null). It was API compatible (with minor adjustments) with the earlier SQLite 2, so the lack of static typing continued, otherwise everyone would have to rewrite their code. You do get dynamic typing, which hasn't been a problem for the vast majority of SQLite users.
Do remember that SQLite is competition for fopen, not Oracle / Postgres etc. It is trying to make things as effective as possible in that scenario. If you don't want numbers in your string column, then don't do that!
