I really miss Ed at GPE.
It's helpful to have an actual electrical engineer who knows about this stuff comment.
Why don't you put massive amounts of GIGANTIC capacitors in your pinball?
Because, unless you consider inrush current, you are putting far too much strain on your components and wiring.
The wiki on Inrush Current is here:
https://en.wikipedia.org/wiki/Inrush_current
By design, capacitors in a perfect world would charge instantly, and use a nearly infinite amount of current to do so. In the real world it takes a little time, but when power is first applied, a capacitor will try to take as much current as it's ESR, the parasitic capacitances, and inductances and suchlike allow.
For 10 milliseconds, current draw is crazy high. Thus in pinballs they have in 'Inrush Current Limiting device' A NTC resistor is a device that is selected to match the expected (high) inrush current of the capacitance expected in your power supply.
If you add a lot of extra capacitance, you will be adding a lot more inrush current, and for the first 10 milliseconds, the current draw can exceed the NTC, the fuse, the Bridge Rectifier's tolerance, (if the cap is after a bridge rectifier), etc.
Bottom line is... you are changing the circuit. Circuits are designed with tolerances, and will probably be ok, or won't fail immediately if you do something unwise.
It's your machine, but inrush current can be remarkably high... like potentially melting wires and starting fires in your house high when you are charging ridiculous amounts of capacitance with no consideration to the inrush current.
I'm not an electrical engineer, if anyone else could chime in here about what you would want to do when doubling capacitance in a pinball, I'd appreciate it!
I've always thought that this is one of those that if you don't know what you are doing... don't do it.