1. Let there be a file F. F is released to the public under 0BSD.
2. Let there be a project P. P includes code from F. The license notice of F is scrubbed as part of the inclusion process.
3. P is released as CC0.
The author of P cannot release the project as CC0 because the author has no right dedicate another person's code (F) to the public domain. Because 0BSD doesn't cause a public domain dedication in jurisdictions that accept doing so, F would have to continue being separate and explicitly exempt from the effects of CC0 to be an accurate of its usage terms. Effectively, this makes 0BSD be a de-facto attribution license in a CC0 project. In practice, it makes no difference, but it's legally deeply inelegant.
Github is the de-facto default sourcecode plattform. If it isn't a standard option on Github then it doesn't feel like a standard license.