Call it a failure-of-imagination on my part, but I can't see any good reason for having a law like that; it gives of the vibes of wanting to protect an establishment based on discrimination.
It's not so much a law but it's such a well-established custom that it might as well be a law: send your application in without a photo and it's pretty much guaranteed to be discarded.
But given that traditionally you always have a job interview before being hired, I don't think that there's much discrimination going on: your face will be known sooner or later anyway.
Call it a failure-of-imagination on my part, but I can't see any good reason for having a law like that; it gives of the vibes of wanting to protect an establishment based on discrimination.