When only a log destination is selected that is not built-in (e.g. file, console) then log messages that occur before the module providing the logging sink do not go anywhere.
This is noticeable when only syslog logging is enabled, for example. Messages logged before mod_posix loads are not recorded.
A possible fix is to prioritize the module selected for logging (probably we would have to switch to e.g. a mod_log_syslog name format), and ensure it loads before anything else. Or to buffer messages from startup until the logging sink is ready.