The caps were way, way excessive for the application, I was just having fun putting them in. And they didn't just smooth out the power, they were capable of running the amplifier for a few seconds. (It was a 125 watt Universal Tiger amp.)
I do know that caps decay over time, but have no idea how that compares with batteries. I expect, though, that long life caps could be built.
I also wonder about using inductors instead. They are, after all, just a coil of wire.
I feel like you're asking the equivalent of why we use DRAM instead of SRAM, or spinning rust instead of flash. And I don't want to shout that down because, as in the latter, constraints do change. But the current state of things is fundamentally based on a cost tradeoff.
Perhaps in the future we'll have supercooled inductors providing power storage, and not requiring periodic changing the way say batteries do. Alas, it's just not right now.
As an aside, it's amazing how little power it actually takes to produce worthwhile sound out of modern speakers. I once wanted to test some tower speakers without a proper receiver around, so I wired up a breadboard with some stupid opamps around poorly-heatsunk transistors, powered by a lab supply. The speakers turned out to be disappointing, but not because of the amplifier!
I do know that caps decay over time, but have no idea how that compares with batteries. I expect, though, that long life caps could be built.
I also wonder about using inductors instead. They are, after all, just a coil of wire.