Though websql, where available, is often faster. It's one of the more common overrides for pouchdb to override the user order in favor of websql where available.
Interestingly, neither Apple nor Google were pro-deprecation; Mozilla, and to some degree Microsoft, spearheaded the move to standardize on IndexedDB.
Moving forward now that Edge is based on Chrome, maybe there's hope for WebSQL after all. Not that it will be undeprecated, but if 98% of the browser market supports WebSQL then it's effectively a non-standard standard.
An attempt was made to break down the SQL dialect and exact behavior of that version of SQLite, but the objection was that it's not really great to reverse engineer a standard from a single vendor implementation even if that vendor's product is open source. (eg. what happens when sqlite changes? do browsers stay fixed on an ancient exact version?)
Though many browsers still support it. https://caniuse.com/#feat=sql-storage