This feature is useful when you want to hide the broadcast from your archive or prevent people from viewing it on the web.
Turning ON Web Version means we remove the ability to view it online in the browser. For example, Google happens to find the email and someone clicks on the link. Well, when they do that they won't be able to view it.
You could also set Archive option on a List
Since you can't "unsend" an email these options may be useful to prevent people from viewing them.