Let's see now. If I remember correctly the energy in a capacitor is
so if we charged up one of those 10 F capacitors to 2.5 V the energy would be 0.5 x 10 x 2.5^2 = 31.25 J or 31.25 watt-seconds. If we power a bright LED using an efficient boost converter we need to supply about 1 W, so we could run it for let's say 20 seconds (assuming we have to stop when the voltage gets down to about 1 V).
If we selected a really teeny low power LED we might stretch this out to about 10 minutes. Also we could scale up the run times if we used more than one capacitor.
I don't think batteries are going to be obsolete just yet, but fun to think about nonetheless...
Rather than take capacitors, which are good at charging up rapidly but low in energy capacity, and trying to scale them to be able to store more energy, a better approach is to start a battery (which already has a lot of energy capacity) and make it able to charge/discharge ridiculously fast.
That's the beauty of the LiFeP04 chemistry: 30C charge rates means charging from empty to full in 2-3 minutes. 60C discharge means it's possible to drain those cells in ~1 minute. This is quickly becoming the new standard for power tools, and probably eventually for hybrid vehicles because of this "capacitor-like" current performance.
Here is an active CPF thread involving a 1000W incan flashlight using LiFeP04 cells.
