I have an ink box and I never wear it with the shoulder strap. But, I still like to carry the box with it's strap around. In my opinion, the strap adds to the shape and look of the box.
I mostly carry my city during weekdays for work, but I like to carry the box on the weekends for shopping etc. It is just the right size for putting in essentials without making it look to stuffed up. Also, I like that it sits up, rather than lie down on its side when I put it on the chair - looks great while lunching with friends!