[RedDevil]

If I read correctly, it is only used to power the electric systems during idle stop. So those don't drain the battery, so that can be kept small.
I fear the system will cost a hell of a lot more though than that heavier battery.

It is no use for a hybrid because they already have that heavier battery to store brake energy to not only power the equipment during idle stop, but also to help accelerate when the stop ends.

Supercapacitors have a very limited capacity compared to batteries.
In the article Mazda claims the capacitor can store 25,000 Joules. The Insight might use up that capacity in 2 or 3 seconds during acceleration.
For effective hybrid use it needs to have at least 5 times the capacity, which I fear will make it too heavy to be practical.

I'd love the properties of a supercapacitor big enough for hybrid use, except the weight.