Capacitors will be great for small items like mobile phones but would be an issue for heavy use such as a BEV. A Tesla 85kwh battery takes around 40 minutes to charge on their super chargers. The cable to the car needs to have a decent cross-section to carry the high current required. This current heats the cable so Tesla are now installing new chargers with liquid cooling meshed into the connecting cable to make the charge time shorter by supplying more current. The issue with charging a super capacitor will be the same but as it can be charged quicker will require even more current over a much shorter time period.
Petrol has around 20 x the energy density of a li-ion battery and is the reason ICEV's can be "charged" in a few minutes.
