Well, if you open-source anything these days and it does make it big, you can be prepared for a flood of low-effort slop PRs that you must either review for free or stop accepting external contributions altogether, making it effectively closed-source. You can't choose to ignore the garbage, it will collide with your stuff, unless your stuff is small enough to avoid collisions (in which case no one will see it).
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.
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.
If by the spirit, you only mean the bazaar model, then yes. But it's in the original spirit of free software. GNU preferred to keep the development somewhat contained, even so many years ago.