Not sure what the measurements are in the US. But in Europe we measure battery size by Kwh. The power divided by the amounts of hours. One kwh is equal to 1kw*3600s (1 hour).
This means that a 1 Kwh battery could run a 1Kw load for one hour, or a 2Kw load for 30 minutes, or a 4Kw load for 15 minutes.
The exception being power banks and computer batteries, which are measured in Ah. The reason being that the voltage is constant (5V), also manufacturers usually use mA so that they can make the numbers look big, like 10 000mAh, instead of simply 10Ah.
I think you are mistaking voltage and power here. It is true that wiring cells in series increases the power, but so does wiring them in parallel. Ohm's law explains this:
Take a 12V 1A cell, if we use Ohm's law, we will see that:
So we know this cell has a power of 12w.
By wiring it in series we double the voltage.
Now the cell is 24V 1A, by using the same equation:
By wiring it in parallel we double the amps but the voltage stays the same.
This cell is 12V 2A, and what do we get?
Now you talk about stupidly high power with no energy. I am assume you meant stupidly high voltage with no amps. This is easily possible, just take a sweater and rub around a bit to make static electricity. Now touch anything conductive. GASP, you just discharged up to around 12 000 000 volts! Now why did the room not explode and the conductors vaporize? Because the current is minuscule, 0,00001mA maybe. This is around 0,12w. Absolutely nothing. You can see this is tasers. You only need 12 000 volts to have a very effective taser, at around 20mA.
Voltage is the pressure in a water pipe.
Current is the amount of water flowing through the pipe.
Resistance is the inside diameter of the pipe.
Power is the amount of well, power in the water. Like the power in a motor, it does not matter if the motor is 6V 1000A or 6000V 1A, they both have a power of 6Kw. (It does impact motor design and such, but that is off topic).
What limits engineers from simply wiring a million cells in series and parallel is the heat generation and BMS. Example of a Tesla battery pack:
Yes, they could have simply hooked a super capacitor to the grid that lasts for 0,1 second like you mentioned.