Well they still have a finite life and are less replaceable than a battery. Even if it quadrupled the lifespan (which is a reasonably generous estimate given OP’s 4-year duration and wikipedia telling me supercapacitors last 10-15 years), it would still eventually need to be replaced and that would generally require resoldering it.
I think a much better solution is 2 battery slots, one to be a backup battery, unused, and then when needed, an LED on the mobo can be turned on. Honestly OP could jury-rig up a similar system if he wanted to, although it’d be a bit ugly and anytime something is jury-rigged I don’t really think of it as reliable.