The technology is there.
I wouldn't be surprised if it continues to evolve in some way. They certainly recgnise the presence of a face and have been able to suggest an identity with some accuracy - providing you can see enough of the face. The technology is impressive in its ability though. Both companies have acquired facial recognition companies in the recent past.
See here: Facebook acquires facial recognition startup, may broaden tagging ability
Many users express themselves through their profile picture
This is a great example: 10 Creative Uses of the New Facebook Profile [PICS]
Users might find it concerning.
There were concerns about whether users would find it creepy/worrying. Plus some legal investigations. See here:
While I can't find any handy references, I've witnessed some user backlash by Facebook users when they feel an avenue for expression has been removed.
When designing online communities / social networks we strive to engender a sense of ownership. This is a signal that a legitimate community has formed. The stronger this effect, the more valuable your network is. One resulting effect is resistance to change.
e.g. Surviving Sudden Social Network Changes
However, some networks are based (or gain an identity) through restrictions.
To list just 2 wildly different examples:
I'd recommend that any restriction fit within the 'story' of your network. It must fit with the understanding of how it works and what it is for. For example if you ensure the profile picture is of a certain quality you can use this as a point of quality or security.