I wonder why until now there is no flash with battery "lithium ion" as well as existing cameras ... Must be because of the real risk of the battery exploding with drainage of large amperage in short time. However, the batteries "lithium polymer" drain amperage allow up to 30 times greater than the nominal amperage in a short time. So far, they are only used in model aircraft engines. Batteries are expensive, but has the best power to weight ratio currently.
The chemistry of Li-ion/Li-Po batteries isn't optimal for high-drain short-duration current draw like filling a capacitor, but rather for moderate-drain, more sustained current draw.