Many sites find that it is important to ensure that mail is sent and received with close to a 100% success rate. While examining syslogd(8) logs is helpful, the local mail administrator generally needs to see the headers on bounced mail in order to determine if the mail was undeliverable because of user error or a configuration error on one of the systems involved.
Defining POSTMASTERBOUNCE results in a copy of each bounced message being set to the person defined as Postmaster for the system.
Unfortunately, setting this parameter also results in the text of the message being sent to the Postmaster, which potentially has related privacy concerns for people using mail on the system.
Site postmasters should in general attempt to discipline themselves (or do so via technical means through shell scripts that delete the text of the bounce messages they receive) from reading mail not addressed to them.