If you're going to run the database in a background process, you may as well run MySQL or one of its derivatives, or Postgres. More concurrency.
You're right, there are use-cases where SQLite is not appropriate. But nothing beats the ease of installation/backup/maintenance of SQLite compared to server databases like MySQL or Postgres. Another point is development: For unit-tests, I found that initializing a SQLite database for each test-run is much easier (and faster) than having a VM that runs Postgres/MySQL/etc, which I have to spin up and tear down before/after each test run.