Based on the other replies about MySQL being simpler and faster, it makes me wonder again why SQLite didn't win.
Also, SQLite is embedded, not client/server. That means that the application needs to run on the same machine that holds the data. And because there is no server to coordinate access, concurrency is necessarily limited.
On the other hand, SQLite arrived just in time to get picked by smart phones, and is consequently the most-deployed database software in the world. There are far more instances of SQLite running today than there are MySQL instances.