0BSD is actually incompatible with a desired pure CC0. Unlike CC0, 0BSD keeps copyright intact. It's just a license with no conditions except the usual disclaimer; CC0 attempts to cause a public domain dedication wherever possible. Consider the following:

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.