You're underestimating the amount of energy you would gain when you factor all of the braking you do. Think of a clock. Manpower winds the little spring in the movement and runs the clock, in some cases eight days and others as 31 days
As crashfrog points out, there is a substantial physical difference between a few grams of plastic or metal and a tonne of it.
That tiny little spring is not moving much at all. It's only there to provide energy for a few grams of metal in total. And a few grams of metal moving very low speeds needs bugger-all energy.
I'm not underestimating the energy stored by using a spring or other elastic-energy mechanism at all. If anything,
you're underestimating the energy contained in a tonne of car moving at dozens of metres per second.
For example, your car's suspension springs.
They weigh several kilograms each and can store enough energy to lift your car a few inches when fully compressed.
Now scale that upwards until you have a spring which is large enough to store the energy transferred when braking.
They would have to weigh several hundred kilograms in total, and that's
only accounting for stopping at the traffic lights if you car is moving at the standard 35mph/50kph urban zone speed limit.
Increase the speed to double that -- the open road limit -- and you have increased the energy of your moving vehicle to 400%, because that's how kinetic energy works: double the speed or velocity means quadruple the energy (assuming the same mass).
That means you need 400% of your several hundred kilograms to stop a moving car at open road speed; let's not even discuss a large transport truck or a semi-unit.
Your car would need to carry a couple of tonnes more steel. There's simply no way to make that economically justifiable if you consider the force required to get it moving in the first place. A V6 in your new Toyota is now as useless as putting a four-stroke in the old one.
And okay then, try aluminium or even carbon fibre. Guess what? Your vehicle might only adding one or half a tonne instead of two now, but it also must be twice the size to fit that material in.
Sorry, Buz, people have thought about this before. They run into the problems described above. It just doesn't work.
{abe: you may have missed out half a sentence in your last paragraph, Buz. There's a single word following the comma, then just a space and a fullstop.}
Edited by Nij, : Noted in message.
Minor grammar changes.