Zero-contribution open source doesn't at all make it closed source.
It delivers on the value of open source, that anyone using your software is permitted to make and distribute their own changes.
SQLite is an example of a project that is open source but closed contribution.
Maybe, but that's hardly comforting (and definitely not in the spirit of open source) if you're forced to take that decision, knowing it will hurt your project, because the alternative is getting DDoSed.
Minor correction: SQLite is not closed to contributions. It just has an unusually high bar to accepting contributions. The project does not commonly accept pull requests from random passers-by on the internet. But SQLite does accept outside contributed code from time to time. Key gates include that paperwork is in place to verify that the contributed code is in the public domain and that the code meets certain high quality standards.