I haven't ever responded to someone on a dating site unless they have some picture of themselves. It doesn't matter how interesting their profile seems to me, I just know I can't get enough of a sense of them without the picture to go any further - and there's something a bit off-putting about knowing that they can see me but I can't see them (just like you've said).

My pic is of me facing away from the camera, so that hits the balance between showing something about myself without feeling like I'm on 'stage' here.