rmdir -v writes always writes STDERR

[Mi]

I expect rmdir to report only errors to STDERR.

When used with --verbose, successfully removed directories should be 
reported to STDOUT, but they are not. They also go to STDERR.

This doesn't seem consistent with other utilities or with the purpose of 
having both STDERR and STDOUT.

An example of why this is an annoying problem:

I do various cleanup tasks in a cron job. STDOUT is redirected to a log 
file, and cron mails me any output on STDERR so I am notified in case of 
errors. This is standard cron behaviour.

With rmdir, I have the choice of either getting a useless daily mail 
reporting successful operation, or also redirecting STDERR to the log file. 
Or suppress verbose output and having no trace of removed directories.