I believe it is already possible to post as an anonymous user. I could be recalling incorrectly though, but if I am not this would be terribly abused. Users could violate the rules anonymously and community/staff wouldn’t know who it is.
Discourse also allows for hiding profiles already too. But some forums disable it. My profile is hidden on here too for no apparent reason. This would also break SEO if you could opt out of search indexes.