At the time sqlite was written, the author of sqlite was heavily involved with tcl, a dynamicly typed programming language. Sqlite also started out as a tcl extension. Having the database match the typing philosophy of the language it was supposed to be thightly integrated with probably seemed like a good idea.

One nice thing that sqlite being dynamicly typed allows for, is having a key-value table for storing singleton objects, like project config (as opposed to having a well defined table with a single row).