Delete all posts by user

There should be an option that allows an admin to delete all posts made by a certain member. 

The argument I've heard against this is that it leaves confusing gaps in topic threads.
On some forums however, the post number within a thread is displayed for each post. Users quickly figure out that gaps in the number sequence indicate a deleted post and are less confused by the other posts in the thread.

Forums that can delete all individual posts for a user also will usually have the capability to delete all threads started by them as well.