Why? Because when I switched, I was in lots of pain. Could barely type at all. I therefore needed to be able to type again as fast as possible, by any means possible -- and so, at the same time I switched keyboard layouts, I purchased an ergonomic keyboard. I've since used Dvorak on flat keyboards, of course2, but I can't tell you how much of my wrist pain was directly connected to the keyboard layout, and how much of it was fixed by the ergonomic.
My wrists are totally better now, since switching both layouts and keyboards. I'm pretty sure that the entire benefit came from the keyboard itself (I use one of those curvy, split ones -- the plain old Microsoft Natural3), and not from the Dvorak layout.
Don't get me wrong -- I love that my fingers move less on the Dvorak layout, and it feels much more ``natural'' than QWERTY ever did. I'm just not sure that translates directly to decrease of wrist pain, or finger pain, or whatever kind of pain you're having.
Who knows -- maybe someone will do a study some day, and discover that Dvorak users were able to type for 10 years longer than QWERTY users, that they ate more brown rice and granola, tended to be vegetarians with left-leaning politics, and made the world a better place. I'm just not sure of any correlation, that's all.