Log output to syslog
This is not possible natively. You could write a Drush commandfile, and call drush_set_context('DRUSH_LOG_CALLBACK', 'my_log_function'); to intercept log messages. See drush_log() for details.

A pull request could be considered; it would need to fail gracefully if someone attempted to use it on a system that did not have syslog. Drush avoids platform-specific features where possible, though, which is probably why this has not been added as a standard feature to date.