Which was the right choice, web standards shouldn't be tied to a single project.
Therefore, tying a standard to a reference implementation, especially one as reputed as SQLite, might not have been a bad outcome overall.
[1] https://hacks.mozilla.org/2010/06/beyond-html5-database-apis...
Alternatively, you need to pick a small stable subset of SQLite functionality to expose. But that would mean you can't just use plain SQLite anymore - you either need to modify it significantly, or need to wrap it somehow. Which either way adds a lot of overhead again.