I think just about any police officer or DMV will tell you that a drivers license is a priviledge, not a right. If she doesn't want to show her face then no drivers license. It's easy - she doesn't have to show her face and the state doesn't have to take her picture!
Oh, but I forgot this is about imposing one's beliefs on the government and forcing everyone to sacrifice their rights to have safe driving regulations enforced. It's all about me!!! (whine, whine)
You're kidding yourself if you think that the drivers licensing system is anywhere near being about "enforcing safe driving regulations."