It doesn't matter what you do here, if someone wants to reject someone based on gender, race, etc, they can do so easily and just say they weren't good enough. This is the ultimate elephant in room with hiring and it's always been there and always will be unless we somehow do hiring while never talking to someone or seeing them or knowing their real-name.
Even if it wasn't expressly forbidden under law, no one was ever rejecting someone from a job "because they are black/white/female/etc/etc/", that's always been obviously wrong, but it's easy enough to simply say "They're not a culture fit." or "Not experienced enough" or "Didn't answer the technical questions well enough."
I don't think banning people's faces on resumes or CVs would fix anything, the only thing that would "fix" this is changing our implicit and unconscious biases from childhood onwards, i.e. a major change to our teaching culture, and across all the media, TV, movies, books etc.
This site could even, when it gets up to supporting some social graph, separate the two views, HR is using bookmarks/folder organization/some other means of solving that problem anyway so "photos key to memory" is irrelevant
I'll give you an argument against optional headshots: Adverse selection.
Given the advantages and disadvantage of having a headshot, most of the folks omitting them will have good reason to do so. Which means that those who don't have a headshot will be disadvantaged further.
IOW, not having a headshot signals one of three things: "I care about my privacy more than most people", "I couldn't be bothered to include a headshot", or "I am a member of a group that experiences prejudice based on superficial characteristics, such as weight or race, and wish to avoid this". There is a long tail of possible reasons and variations on these, for example the privacy one could actually be more along the lines of "I am hiding from my violent ex", but you get the drift.
None of these possible reasons are ones that give a reader warm fuzzy feelings. If the profile owner is very lucky, the reader will treat the absence of a headshot as largely irrelevant metadata, but that's the best case scenario: one of merely avoiding negative associations. There is no actual upside (the one exception I can come up with is an employer actually looking for candidates who are fanatical about their privacy for some reason, perhaps for security-related positions).
At least when you include a headshot you are only going to get hit with the actual relevant prejudice (which is a social filter that can be useful to you), rather than a stew of prejudices attached to all the imagined or assumed reasons for the image's absence, none of them consciously or coherently articulated.
...unless the "I would experience prejudice" reason is correct.
I'm in the UK, where race, age, gender, religion, disability are among protected characteristics. As such, that information, should it be included, is often either stripped from the CV automatically or the CV discarded entirely to obviate the risk of being accused of discrimination.