Which then begs the question why can't we charge the capacitors with electricity from a fission power plant when it has a higher energy density than solar energy collectors...
Indeed.
Demonstrably, this "can't happen", because if it could, then well, it rocks the entire jump ship economy.
Alternate energy sources (solar, fission, fusion, anti-matter, coal fired power plant on the planet surface), alternate fueling sources (drop tanks, fuel shuttles, "tankless" jump).
When you don't need to charge the capacitors in "a few minutes", but can take your time (hours, days, weeks), all sorts of options open up. Traders can start recharging their capacitors as soon as they leave Jump, and charge them continuously while off loading and onboarding passengers and cargo. Ideally having a power plant size to where the capacitors will be ready to jump by the time all of the other sundry port business is done. "Hey look, we just freed up 40 DTons of space!".
Military ships might have the massive fuel load to "jump fast", but perhaps less so everyone else. It also allows for better handling of emergencies.
"Yea, we misjumped, we're in a dead system, and the jump tanks are dry, but if we ration, we can get J1 charged up in to the capacitors from the main power plant over the next few weeks. It's going to be cold and lonely, but we can do it and get home."