Why? SQLite is one of the highest quality codebases out there! For fun, sure. But I think you are underestimating the size of the SQLite project and it's tests. Just because the library is small it doesn't mean it's simple.
That said, it's one of the most reliable projects in existence so why rewrite it?
IIRC Mozilla's main gripe with it was the fact that there was only one implementation, and no standard beyond "Whatever Sqlite3 does".