I do support and have practiced the destruction of anonymous letters. However I will add that there is a risk in destroying any information (even anonymous) without review. The review process is to protect you, the organization, and possible victims, based on legal issues that may come into play regarding the content of the letters. Alleged issues such as sexual harassment, embezzlement, and other illegal acts carrying the potential of harm and/or responsibility must be considered. I have often said “the only thing you cannot do with this type of information is nothing”.
My bottom line is that I have trashed numerous anonymous letters, but there have been some that I acted upon when it was the prudent thing to do. Never say never when you are dealing with thousands of students, hundreds of parents, and dozens of staff under your leadership.
Think. Work. Achieve.