Not OP, but with supercapacitors you're talking about a wildly different amount of energy. A 5F/5V cap stores about 62 J, while a 2500mAh 1.2V AA battery stores 10 kJ. With three of them you can store almost 500x as much energy.
You don't need that much of energy to keep CMOS memory and RTC clock running. The battery will self-discharge way before it's exhausted by the load. IMHO.
Super capacitors have very high self discharge rates relative to a lithium battery. For something like an RTC which only uses a tiny amount of power, you’d quickly discharge the cap and have no way to charge it again.
Supercaps don't not leak and do not require to be changed regularily. Yes, offline time on supercap would be small, a couple of months, but for a machine which is used often that is not a problem.
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