Why Reuse Design?

Because gas is cheap. In a world where gas is expensive, regenerative braking technology makes a lot more sense, and automakers invest the time and resources needed to prototype alternative means of storing energy and recovering a car's momentum instead of turning it into heat.In a world where gas is cheap it doesn't make any sense to bother. It's cheaper to spend the gas than to design the system. Of course, advance a plan to stimulate the development of these technologies via gas tax that makes gas reliably expensive, and it's all "tax hikes on the poor!" and "global warming is a hoax!" mostly from your side of the aisle, Buz.

The gas needed to push that extra weight around would more than swamp whatever gas you saved by regenerating momentum after braking.

You don't gain any energy at all, you just expend less gas from a traffic stop - theoretically. But the elastic mass adds weight to the vehicle, weight that you have to push around all the time when you're not using it. Are you aware of any clocks that have 2000-pound hands?Physics, Buz. It's a real thing, honest.