I know I wasn't directly addressed with the buckle question, but having played around with it a bit, I believe it is to keep the buckle from biting into soft flesh when doing substantial bending at the waist (picking something up off the ground, etc).
Being right handed, I found it easier to cinch up over my right hip. May not be an issue for people with less frontal abdominal protrusion than I have.
With jeans, the buckle in front isn't a big deal since the fabric is thick and "sturdy" to an extent. With a single layer of linen, it was much less comfortable. I haven't integrated a strap and buckle *in* my braies yet, but I did try with just wearing a simple belt over top of them for experimentation, both in front and on on either hip.