"Also capacitors hold their charge for seconds at best....for the largest ones....."
You're rather ignorant of the properties of capacitors, then.
Actually, the big ones are capable of holding a charge for a couple days after being shut down.
You know, the big ones, like those on induction furnaces, that could blow you to smithereens if you bridged the connection. Those ones.
That's why, in fact, that even consumer electronics with capacitors (e.x. power supplies) are a bit dangerous to work on if the capacitors don't bleed.
Capacitors are great at outputting all their potential really really fast. That's why they haven't replaced batteries, but come in alongside them, in, say, electric vehicles. The capacitor gives it the power it needs for acceleration, and the batteries keep it charged and keep the vehicle at a constant speed.