THat's an interesting idea, for a very short time I guess (like those caps that hold an LED on for a couple seconds.I guess it didn't cross my mind because I think the energy capacity of a typical capacitor (.5CV^^2) seems so small for a capacitor circuit that is going to be less than a gram, and is supposed to charge a battery which probably has a much larger capacity. I'm not sure what the circuit would look like for a voltage >> 5, and I'm not exactly sure what sort of regualtor chip (which might need it's own voltage supply or external components and have it's own operational limits) you would use here. THe LM317 (which I know is sort of hefty) weighs over a gram itself. And then at the voltage you are talking about, what about heat dissipation? If you're running a V>>5 volts through it at that current, it might get hot.
You're probably going to have to regulate the voltage and current if you want to keep them within limits, otherwise I guess you could just use an RC circuit. Anyway, I'm not sure how practical this setup would be.
I suppose it might be possible to hold some voltage on that battery for a little while using this method though. And there may be some sort of supercomponents around they can use. I'm just remembering all this stuff from the old days - they may have a lot of fancy new stuff these days.