Of course, there are other ways to stop fraud which you'd want to do as well.
They could charge for "Verified by Facebook" services. Hell, they could replace eBay and PayPal while they're at it, not to mention AirBnB, CraigsList, etc.
They're stumbling around looking for a business model as it is, I don't know why they don't get into this. Sure, easier said than done maybe, but if anyone can do it, it is Facebook. Becoming the one site that has the single largest repository of known internet identities within it is the hard part.
So bizarre to me they don't move into in a serious way. ecommerce