but the capacitor's voltage is directly proportional to it's charge state, in other words, as soon as the rtc (or anything else) starts to discharge the capacitor, the voltage will be going lower and lower, while on a battery the voltage will not change(coarse as the cap) as long as the battery have a reasonable amount of charge (at least 5%), so we must therefore have to have a specific rtc that operate in any voltage from 0.5 to 4vdc
also a capacitor of the size of a C battery still holds less energy than a AAA sized battery (to be exact, any battery actually sold holds more energy than a capacitor of the size of a C battery) so definitely a capacitor is huge
ultra-capacitors can be used, but they are pretty expensive and hard to buy (at least on a third-world country)
we can use a capacitor to hold rtc for 2 to 5 minutes while you change the batteries, that would be no problem I think, but still a cell-shaped battery (that tiny one) would take less space and hold it up for hours, altough they're not rechargeable