Consider not adding a CakeBuildLog as fallback to all loggers

Is it real world use case that a build system logger is registered after checking the respective environment variable and that changes throughout execution?

Does it really need to be checked on every log event and have a `CakeBuildLog` fallback?

Start by locating the logger registration, the environment-variable check, and the CakeBuildLog fallback mentioned in the issue. Trace how those choices affect each log event, then establish whether registration can change during execution and define the expected behavior before adding focused coverage.

Written by the indexing model from the issue text.