I think this is useful for libraries in a language like C, where there is no standardized logging framework, so there's no way for the application to control what the library logs. But in a language (Java, Rust, etc.) where there are standard, widely-used logging frameworks that give people fine-grained control over what gets logged, libraries should just use those frameworks.

(Even in C, though... errors should be surfaced as return values from functions causing the error, not just logged somewhere. Debug info, sure, have a registerable callback for that.)