Supercapacitors have been "the coming thing" for a couple of decades. Their advantages are obvious - far higher efficiency than any battery, far longer life than any battery, almost zero self-discharge, use no strategic materials, and very high rates of charge/discharge are possible.
But there are a few disadvantages - As Bee Utey says, the terminal voltage varies directly as the state of charge, which, while it complicates the electronics, does make it easy to measure the state of charge.
More significantly, manufacture of them is relatively expensive compared to batteries, and they are physically fragile compared to batteries (supercapacitors, not capacitors) because to get the "supercapacity" means having both the dielectric and the plates very, very thin. And physical damage can mean very rapid self discharge, with serious safety issues. I don't think that currently they are able to match lithium for either energy/kg or energy/cubic metre, but except for vehicles, that may not be an issue.
John
JDNSW
1986 110 County 3.9 diesel
1970 2a 109 2.25 petrol
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