Is there any battery chemistry that can compete with gasoline on energy density?

You are thinking in terms of a vehicle that is powered by a supercap. That would almost certainly never be the case, especially due to the -1 discharge potential profile of supercaps (compared to batteries, which are near zero). A vehicle would have scores, even hundreds of discreet units, not a single enormous supercap, so the likely energy release from a breach is never going to match anything close to the vehicle’s full capacity.

Would that be something like a lightning bolt strike?

A lightning bolt has a few GJ of energy. That’s not unlike what you’d be storing in a very large capacitor if you wanted to use it as your main energy source in a car. I would definitely be concerned about the possibility of all that energy finding its way to ground abruptly.

I think the point about the potential power (rate of energy flow) of an inadvertent energy release is good; it is, after all, the power and not the total energy of accidental events that makes them dangerous. A thunderstorm, we’re frequently told, releases more total energy than a (small) atomic bomb – but it does it over hours, not microseconds, and therein lies all the difference. I don’t think the point can be easily dismissed by noting that all storages of large amounts of energy are dangerous. They’re not equally dangerous, and the rate of potential energy release is a pretty important factor in how dangerous they are.

Yeah, no.

Apparently cars have batteries in the 60 kWh region, which is 60000 W * 3600 s = 216 MEGAjoules.

Also, the electricity isn’t going to flow toward ground. The electrons are going to flow from the anode to the cathode.

Lithium-air batteries are an interesting prospect, if the technical details can be worked out. According to the wiki thing, fwiw, they have an energy density that is realistically better than half that of gasoline per Kg and can be reconditioned electrically, meaning an individual theoretically could have a reconditioning unit in their home/garage. At two or three hundred miles per unit, one could have a vehicle embayed for eight or ten units, have several batteries in the shelf or reconditioning at any given time, and only load the vehicle with the number of units needed for the time being. With the potential for more than two thousand miles of range with all the bays loaded with battery units, most general usage needs could easily be covered. On a longer trip, the traveler would be able to find some location where they could do a battery swap.

The biggest downside to metal-air batteries is that they get heavier as they discharge, which is the opposite of what happens when a vehicle burns fuel. But that could be handled simply by making remaining range estimates very conservative.