I make a lot of instrument straps, Guitar, Banjo, Dobro, Mandolin, etc. I cut my straps from sides, and it works well for me. With the right draw gauge it is pretty simple to cut straps once you cut a straight edge on the side. My straps are made from 3-4 ounce leather, so I normally buy belt blanks becuase I don't make nearly as many belts as I do straps and the belts are normally thicker.
Ken