It should be compatible with most DBs, but SQLite has more dynamic types, and supports more things, in ways that are "odd" for almost all other DBs. As you correctly said, in general, no two DBs are easily interchangeable, and SQLite is no exception, perhaps it is even more of an outlier in fact.
That means that to implement SQLite, not using SQLite code, means you need to carefully reproduce that behavior, and all aspects of it - in practice, including bugs - to be a compatible web browser. For a web standard, that's just unacceptable.
http://www.sqlite.org/datatype3.html
It should be compatible with most DBs, but SQLite has more dynamic types, and supports more things, in ways that are "odd" for almost all other DBs. As you correctly said, in general, no two DBs are easily interchangeable, and SQLite is no exception, perhaps it is even more of an outlier in fact.
That means that to implement SQLite, not using SQLite code, means you need to carefully reproduce that behavior, and all aspects of it - in practice, including bugs - to be a compatible web browser. For a web standard, that's just unacceptable.