The problem is that hiding your picture results in far fewer messages, by a factor of eight.
I don't doubt it. There is no point in messaging someone without a picture. You could be talking to a land whale for all you know. There are some seriously fat, ugly women out there, and a high percentage turn to online dating as men find their appearance so revolting in real life. Attractive women are getting laid the old fashioned way. There's no need to get computers involved.
You also gotta watch out for "myspace angles" type photos. Be vary wary of a woman without arms, hands, or body in the photos. Chances are she outweighs you if you don't see that stuff.
I know a woman who works in IT across the street, while cute, she's about 150 pounds overweight. I ran across her on OkCupid (blocked her right away) but her photos make her look MUCH better than she actually is, even though there are lots of them. Somehow, she either used old photos, or manipulated the photo (pre or post snap) to remove her gigantic gut.
I expect the women with NO photos available are either cheating, or way worse than that. I skip right over them, and my first response to being messaged by one would be "put a picture up in your profile or fuck off".
Like it or not, physical beauty is tremendously important to most men. If you don't have it, or won't show it, you are going to be last in line out of the gate.