This is funny and sad to me. We had SQLite in the browser[0]. I only did a little bit of work with it but it seemed actually pretty nice. It was torpedoed because it was SQL-based (and not trendy "key value" and "web scale"). There was the whole excuse that the specification was "whatever SQLite does" and, therefore, not suitable for being a standard. There would be worse things than SQLite upon which to base a stand…
Using SQLite results in a new, built-in reliance on a C library. Even though most languages can use C library bindings, it does present some issues in some build scenarios, such as static builds, and, given the enormous scope of SQLite, would prevent anyone from ever achieving a 100% rust browser.