A full wrap is the best thing since sliced bread, at least when it comes to a falling saw. Even if you don't have to double cut the tree, it's easy to make all your cuts from one side of the tree. It makes it easy to fine tune your holding wood when you're gunned at the same point in your back cut as your were in the face cut.
We also have some trees that are big enough that even a 36" bar requires double cutting. It just gives you more options and makes lining up your cuts that much easier.
I'll also add that it's a big deal for climbing with a rear handle IMO. It's really nice to not have to move around, or contort your body when bringing down a spar.