The biggest problem is that yeah, WebSQL tends to be faster than IndexedDB. Or at least it was back when I was working on PouchDB. Biggest issue IIRC was that joins were faster in SQLite than implementing the same thing in userland on top of IndexedDB. Browsers eventually shipped getAll/getAllKeys which also helped with cursor slowness.
I haven't looked much at the Storage Foundation API [1], but it seems like a more reasonable approach moving forward. Just give developers the low-level tools and let them build SQLite on top of it. Also the Chromium devs have been working on relaxed durability, which apparently improves IDB perf in some scenarios [2] (although still not as fast as Firefox it seems [3]).
[1]: https://github.com/WICG/storage-foundation-api-explainer
[2]: https://www.chromestatus.com/feature/5730701489995776
[3]: https://bugs.chromium.org/p/chromium/issues/detail?id=102545...