Think of it in a structural sense, and your objective. Start with the basics. You want to keep your cock (and more importantly, your balls) from bouncing all over the place when you're being physically active, for the purpose of avoiding the discomfort of having your balls bouncing around.
So, you have your pouch. You've got to anchor it to something. You anchor it to your torso at the top via a circumferential band. OK, that leaves the bottom of the pouch not secured. You could do that with one strap, yielding the thong. But not everyone likes a fabric strap between the cheeks of your butt. So, add one more strap. Now you can angle them off. You've got to anchor them to SOMETHING at the other end. I suppose you could just loop them around, around the top of the leg and back, but it's simpler and just as stable (and uses less material) to connect them to the waistband you already have.
Voila! You have just (re-)invented the jockstrap!