BTW, Welcome to ETO, Sam5253!
I think the major downside of using caps (of whatever flavor) as a "battery", in particular as you envision, is that their full voltage level immediately starts to drop from its peak as soon as a load is applied. This has the effect of, in a like manner, of quickly reducing the power transferred to the load, as graphically represented in the graph in post #3.
This effect can be lessened, to a degree, by massively over building the circuit by increasing the total capacitance to, in my opinion, ridiculous and very expensive high values for automotive use.