Contemporary Amperex Technology Co., Limited (CATL), the largest battery manufacturer in the world with a 38% share of the global market, has just announced some fairly significant breakthroughs in battery tech that aren't just theoretical; they're already hitting the market.
Electricity is not my forte so correct me if I’m wrong but if you had a long gap in cars using the charger a capacitor would quickly become saturated. Which means you would need more wattage going to the capacitor at all times. Whereas with a battery if you have a car on a 5 minute charger with 5 minutes in between you could pretty easily run 500kW constantly to the battery and then as the battery dropped in level you could slowly ramp up the power draw