Charging a Tesla in ten minutes would require dangerously high voltages, or ponderously heavy cables to carry the current, or both. But the capacitors would limit the amount of voltage that could be applied, so you're left with ponderously heavy cables.
The ZENN electric car company (which made a very nice electric car back in the days when your choices were a DIY conversion or a 35-mph NEV) went bust when they believed EEStor's hype about super-capacitors and invested in the company.
One problem with super-capacitors is that if the dielectric is breached there's an explosive release of energy. A super-capacitor pack big enough to power an electric car faces very real engineering challenges to make it safe. If the pack fails in an accident it would be a Hollywood action-film-maker's wet dream of an explosion.