There's nothing wrong with implementing the actual standard IndexedDB on top of SQLite, since it's entirely possible to reimplement IndexedDB on top of a different underlying database.
WebSQL would have been awesome right up until the moment that some new platform takes off where SQLite won't meet the requirements for but we want to reach with the web platform, at which point we'd be screwed. Or even worse, WebSQL would guarentee that the reach of the web platform has been fundamentally limited by what a single codebase can reach.