I don't think it has been attempted either. The caps are there as they are long term more reliable than a battery would be*, no high current needs or anything like that (not that most supercaps do well with high draw) and if the device is only needed sporadically for a few seconds each time (and then gets power once it is done) then caps can be justified as a design decision.
Do remember to check what voltage the whole arrangement uses -- most supercaps are really low voltage limit so in practice designers will often series wind them to double the voltage limit (and half the capacitance).
*see also all those game carts that need battery replacements, most N64 memory paks, most rechargeable devices over about 6 years old and so on and so on.