IndexedDB has terrible support. Sadly LocalStorage is the only reliably supported option right now. I really hope in 6 months this comment is wrong.
--EDIT-- sorry @untog, I replied to the wrong comment and deleted before as you replied.
--EDIT-- sorry @untog, I replied to the wrong comment and deleted before as you replied.
Also - these fallbacks are not exactly swappable. Its like swapping from a Database to a Filesystem as a fallback. Difficult to abstract into a single library/api.
And you still potentially leave out IE users if those are your options (depending on your IndexedDB needs).
IndexedDB to localStorage fallback might work - but again might not be an easy API abstraction.
Web SQL may be "deprecated," but it's unlikely to be dropped by Apple or Google, since so many mobile web apps depend on it. Even the mobile version of Gmail uses Web SQL.