But you don't have to place your finger in a choil to place your thumb or finger along the spine to act as a depth stop. And if it is an empty box you are cutting up to put in the trash , you wouldn't have to have a depth stop if you didn't have a choil that the box could potentially fall into and impede the cut.
Ken are you thinking of sharpening choils when you talk of them impeding the cut?
http://img257.imageshack.us/img257/7914/comparisonoc8.jpg
Just so we're all on the same page, the top knife is a sharpening choil, the bottom is a finger choil. I dislike the former because when you cut things sometimes the material will slip on to the unsharpened portion near the handle. I like the finger choil for enhanced control in cuts.
The way I see it, the closer your hands are to what you're cutting, the better control and leverage you have. Basic physics. This is why I've gotten rid of some nice larger knives like the Spyderco Military. If I'm opening a box, peeling an apple, whittling wood shavings for a fire, cutting a loose thread etc, extra control makes the job much easier. I've found it's really rare when an out of choil grip like this is of benefit to me, which is why I got rid of my larger knives in favor of smaller knives.
http://img74.imageshack.us/my.php?image=hammergriptz5.jpg
http://img210.imageshack.us/img210/204/choilgripkh0.jpg
In the second image the hand is about an inch closer to the cutting. This is especially useful when working with the tip.
If I did heavy chopping, dynamic slashing or similar with my folders, I might desire the "regular" grip more. But I just use it for small cutting tasks like peeling fruits and veggies, slicing meat, opening mail, trimming my nails, carving wood, opening packages, slicing plastic shrink wrap, touching up a missed spot after a shave etc. For my uses the enhanced control works very well. The same thing drives my selection of knives for the woods. I found I either needed to cut small things like whittling wood or food prep, or I needed to bash stuff apart like batoning a log for fire wood. Swiss Army Knife + a Kuhkuri works well for me.