Isn't it possible to hide user information on threads if they willingly want to make a post anonymously?

We should have a checkbox on the post-writing screen, somewhere around the "Post" and "Preview" buttons, maybe above them and below the textbox where we write our posts. The checkbox should look like this: Post anonymously: [checkbox]

Those who mark the checkbox and then press "Post", their post should get posted, but all their information should be hidden. The space where user information is shown should only say "Anonymous Poster" with no href, which means the username shouldn't be clickable. There should be no profile or anything behind it.