SQLite is a massive library, with a lot of functionality and optional extensions, and behaviour is added or changed over versions. Codifying all the behaviour into a standard would be a massive effort. And then you're either stuck on that version of SQLite, or your standard depends on what an external project is doing with new releases - which is really not what you want for a web standard.

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.