The problem with anonymous user is that we don't know his email address. If we forward an anonymous user's post to subscribers, it could let spammers spam subscribers and we have no control over it because anonymous can be anyone. Even if you don't mind it, some people do feel strongly about spam, so it's a risk to us and to you as a forum owner.
It might be a good idea, if possible, to have a warning note in the compose area for users that aren't logged in about this—that way they'll know that their posts will only be seen online.