Is it practical to use capacitors as backup power supply?

I saw some 4F 5 volt capacitors at my local electronics store (as audio components) pretty cheap ($10ish). I'm wondering how feasible to use them as backup power in place of heavy batteries? Sure it'll be a bit more expensive, larger in size, but they should be lighter for the same power stored?

Its mostly of illumination uses, maybe a fan or to power a laptop. I plan on using LEDs and EL lighting. LEDs uses low voltage DC, perfect for the low voltage capacitors. EL require higher voltage, but will run on DC also. Fans I have are mostly 12V type. Some 5V and some 24V also. I haven't figured out the laptop part yet.

The main reasons I think capacitors are better than batteries:
Lighter,
100k's or 1m's of charge/discharge cycles vs a couple years for lead-acid, most batteries will die quick from extremely deep discharges.
no acid. Caps are sealed electrolytic.
no maintenance, they are sealed. In storage they are good for 10-20 years in ideal conditions.
no charging limits- unlike batteries I can charge then as fast or slow as I want.
no discharge limits- batteries have internal resistance, they can get hot from heavy discharge enough to kill themselves. its also a bad thing too, sorta makes charged capacitors a serious handling hazard.

any opinions/reasons why it wouldn't work?

-thanks