When you stitch across a strap as you have done, you have effectively made a serrated line, similar to the line between 2 postage stamps.
If you need to sew on a strap, a longer stitch length and only a single pass can be stronger because it has not compromised the width of the strap as much.
You may have seen on some sewn equipment, a strap that has been sewn on to a bag or whatever, where the strap has been sewn in a square around the end. By sewing this way, you have 2 line of stitches across the strap, but they are separated by a piece of undamaged strap. There is also the stitch-line running along each side of the strap, which is the strongest direction and not so likely to cause a strap to fail.