No it's not. WebSQL would have become "WebSQLite", quirks and all. That's not good for anyone. Any quirks in SQLite (of which there are _many_) would immediately become unfixable parts of the spec.
Sure would be a shame if a web standard reified implementation quirks as a durable part of the spec, something which has never happened before in the history of the World Wide Web.
Yes, it would be as much a shame now as it was then. This might come as a surprise but you can actually _learn_ from past mistakes and attempt to avoid them in the future. Like websql.
SQLite is a large, complex project by itself. Not only would you be adding it’s quirks into the spec but you’d be basically locked into a specific version of SQLite that has to be bug for bug compatible with whatever version was shipped before.
It’s quite clearly a terrible, terrible idea. And I say that as someone who was quite looking forward to what WebSQL has to offer. It’s more a reflection on “there is only one embedded SQL database suitable for use” than anything else.