Ultimately a computer network cannot genuinely steal the identity of a person, unless I'm mistaken - they're a person, and their human connections understand that.

With many of today's payment methods, I agree that the payment identifiers are susceptible to being copied in unencrypted environments. However, identification/authentication and authorization are two separate steps - it'd be possible to entrust authorization, for example, to groups of trusted friends/family (with perhaps separate social groups and rules based on category of purchase, amount, and so on).