The downside of strict tables is that some data types are not available, such as Date.

Strict should really be the default. If a database is shared by multiple applications then you should be able to rely on the declared data type. If one application stores a string into a numeric column that breaks everyone else.

On the other hand, the main use case for SQLite is embedded databases. And that means only one application is using the database. In that scenario being able to evolve the schema (as opposed to creating a new database and copying the data over) can be seen as an advantage. The application's code knows what to expect in each column--including mixed data types.