It's not intuitive, but there are definite advantages to using it. Now that I've used it correctly for all of less than 200 shots, I'm going to stick with it until muscle memory takes over and not have to think about it. Just remember to practice.
I did try this for awhile but ended up not using it. Maybe I should try again, it's remembering is the problem. I used to concentrate on framing/lighting etc and then forget to use the thumb for focusing.
Got the AF-ON fever with my D700 and was really disappointed when my D600 arrived with no dedicated AF-On button. Of course, I soon realized that the AE-L/AF-L button could be dedicated to AF-ON. I do a lot of bird photography and the AF-ON focus mode is a blessing. One thing to remember though, you will not be able to auto-focus with a remote or self-timer unless you deactivate AF-ON first - unless you have a body like the D700 which has the menu option "AF Activation -> Shutter/AF-ON".
Today I was shooting historical shots, copies of B&W portrait photos of elected officials. They will be used to make these photos available online for County Archive. Used tripod and live view and remote shutter release. My D600 surprised me by focusing just before the shutter release. I then used the AF - manual switch for each shot because I did not want such a feature for this use, but I can imagine times when this would be great. For example, on tripod near hummingbird feeder, in live view, using remote shutter. Camera could then focus and shoot while operator stayed at a distance to avoid spooking the bird.
Backbutton AF has always been used by photojournalists and sports photogs who often find themselves in crowded situations and don't want simple jostling and body-contact to cause their index finger to release the shutter with unknown focus results. By dedicating the shutter release and AF to two separate fingers, I've always been able to work better next to other photogs and in crowds with less false-fires. Also for cold-weather sports and nature photogs who must use hand and finger protection (which reduces button sensitivity) using the back button AF reduces the chance of shutter button false-fires
It used to be that burning through a 36 exp roll of color neg or trans was an expensive proposition, as it took the F5 at 7-8 FPS only a few heartbeats. No one wanted to have any false-fires, as that cost serious $$$ - but those who use only DSLR bodies today may want to experiment to see just what finger techniques and shutter button release settings work best for you. I still use the shutter button for focusing and shutter release, but that is just for brain-index finger reflex practice with my old age
I've used this for years and love it. One of the nice things, is it keeps you thinking about focus point. Not to distraction, but in a good way. When shooting BIF, you just keep your thumb pressing the button throughout the sequence. Landscape or portraits, just focus, release the button, recompose and fire away. You can recompose and shoot again without worrying about your subject changing.
The only downside is when someone hands you a camera that focuses normally and you realize how weak regular shutter button focus is (control wise...)