Such an ultracap could be useful if correctly integrated into the system.
But do not consider it as a 'bolt in' replacement for a battery.
Just like a battery, care and feeding (charging and discharge) must be done correctly in order to achieve long life.
As mentioned, you cannot exceed the maximum discharge amperage without damage.
And that max rate is determined by the specific design of the UC used.
A capacitor does not discharge instantaneously, instead at the rate is mainly determined by the charge voltage, the load resistance, and the internal resistance. The internal resistance is determined by the design of the unit. High amp devices require specialized (more expensive) construction.
Most UC are rated at 2.5V max, so you would be looking at an array of devices hooked up in series
So a properly designed control circuit is required.
Check this out:
And note this statement from the article:
'Where they're weak, however, is with energy storage. Compared with lithium-ion batteries, high-end ultracapacitors on the market today store 25 times less energy per pound'
That's vs lithium-ion batteries, doesn't say vs lead-acid. And then there's cost.
It will happen eventually.