Many will scoff at the following but here goes-
Full wraps are a West coast phenomenon. Terrain here is uneven at best, and often you'll have to fall a tree from one position because of slope, tree lean, obstacles, etc. (This, and our softwood timber is also why we run longer bars.) Based on having to fall from one stance, you may have to turn the saw over, so it's cutting clutch up. This is where you'd used the full wrap. In my avatar, I'm using my 361 clutch up with the full wrap. The opposite side of the tree was a brush tangle and slope, and no escape route, so I had to cut from where I am in the pic. And for me, as a side effect, it makes the saw more comfortable to carry, as I carry it on my right side, bar backwards. Also, a buddy of mine mills with a 660 with a full wrap. He likes it on the mill because when you lay it down (It's an Alaskan Mill.) it rests on the wrap handle and not on the saw itself. Each of my saws has a full wrap, and they feel natural to me. I cut with another buddy's 036 with a half wrap the other day, and I felt naked without the full wrap.
Jeff