What if those photos do leak information that could enable real-life harassement (like EXIF metadata, street sign, etc) . Can we trust the submitter to guarantee it never will? If it happens, who's to blame?
Those are both nuts. You handle the issue the way adults handle the issue:
1. Say "you can't post X."
2. Count on the fact that most people won't post X once you tell them not to (on pains of account sanction, which are already in place for rules against things like spam).
3. Deal with the complains of false positives and false negatives on a case-by-case basis.
Then they should be removed. Imgur (Reddit's favourite image hosting) already strips meta data.
If there's a face in that image, then there is the identity of a person in that image.