@LisPiThey did start that:
https://en.wikipedia.org/wiki/Web_SQL_DatabaseThe problem was that "sql" is big, so first they would have to agree on a specific set of instructions for a full RDBMS which is pretty much as much work as a browser itself
So they proposed to just use sqlite, which was almost fine except now a standard would only be properly implemented by a single implementation. This is worse than the current web.