Most dating websites are not anonymous, and how can a person be anonymous when they want the picture of you and your face. The face is easily recognizable, easily remembered and might create problems in private life. And without a picture at all nobody knows who is there, so it's no fun.
My idea of the dating website is that it would require only one naked picture of person's body below the head.
Maybe it's a stupid idea. But it's kind of anonymous, but still shows a lot of interesting things. Usually bodies can't be associated in public because they are covered by clothes a lot. This idea in addition to psychological tests might help.