Question

Why fast charging and discharging is needed in supercapacitors?

Answer 1

A electrical power storage device (battery or capacitor) has a certain amount of energy it can store - think volume of water - and a certain discharge rate - think diameter of bunghole. A supercapacitor has a larger bunghole, so charges can easily slide in and out. An battery, though, has a larger overall volume, so you can stuff more charges in. 

So, if you want to use your phone as a taser, it would be great to have a supercapacitor in it. A supercapacitor phone will also charge faster than a battery one. 

The thing you are missing is that the supercapacitor only discharges when you 'let it' by connecting it in a circuit. Otherwise it would probably hold the charge more or less as well as battery.