When there is just a single codebase, even if it is open source, it isn't a standard. Now, not everything needs to be a standard, but on the web standardization is a big part of why it is so successful.
One example of why a single codebase is bad: Imagine that SQLite version X is the implementation of WebSQL, which all browsers must use. SQLite development is of course continuing, fixing security issues and making it faster, etc. Will browsers just keep using SQLite past version X? What if the SQLite community takes SQLite in a direction that isn't optimal for web browsers? Perhaps web browsers will fork it. What if browsers end up not agreeing on the fork, and some use the original project, and others use the fork - or there are multiple forks?
All of that makes it very risky that compatibility issues will appear between browsers. Having a properly specced standard, with multiple compatible implementations, is so far the best way that we have found that can prevent such things.