"Each cell has to carry the same load either way."
This is where we differ.
Ok. At least we're clear on where we disagree.
I'm going to use my system for this example. Let me know if you think it fundamentally different for other systems. I'm going to define each parallel bank of my batteries as putting out 4 volts, though the range is 3.6-4.2.
1) I have 20 banks of 15 cells. Each discrete bank of 15-cells is wired in parallel. I like to call these banks "subpacks". When these banks of paralleled-cells are wired together in series, I call that my "pack".
2) Each cell is 2.2 amp-hours and 4 volts. Therefore each subpack has 33 amp-hours of capacity (15 x 2.2 amp-hours), at 4 volts.
3)I could wire two subpacks together in parallel to create a 66ah 4 volt super-subpack, and I since I have 20 subpacks, I could do this 10 times, wiring 10 "super-subpacks" in series to create a 40-volt 66ah "pack".
4)Or I could wire all 20 subpacks together in series to create an 80 volt, 33ah pack.
5)Either way, my pack is the same watt-hours of capacity. Let's see how many:
a) 66 amp-hours X 40 volts = 2,640 watt hours
b) 33 amp-hours X 80 volts = 2,640 watt hours
this makes sense because I've got 300, 2.2ah 4 volts batteries either way and 300 X 2.2 amp-hours X 4 volts = 2,640 watt hours of energy.
With me so far? Are we in agreement so far?
5)So let's say I'm cruising down the road at 20mph with my 66 amp-hour 40 volt pack. That bike calculator, and my on-board ammeter, both tell me I need to suck from my pack a steady 10 amps to maintain this 20mph.
6)This means that each 30-cell "super sub-pack" is contributing 10 amps at 4 volts and each cell is contributing 1/3rd of an amp (10 amps / 30 cells). The volts then add together for 40 volts at 10 amps which equals 400 watts.
7)So each cell in this 40 volt 66ah pack is contributing 1/3rd of an amp.
8 ) If instead I'm cruising down the same road at the same 20mph with my 33 amp-hour 80 volt pack, that bike calculator, and my on-board ammeter, both tell me I need to suck from my pack a steady 5 amps to maintain this 20mph.
9) This means that each 15-cell sub-pack is contributing 5 amps at 4 volts, and each cell is contributing 1/3rd of an amp (5 amps / 15 cells). The volts then add together for 80 volts at 5 amps which equals 400 watts.
10)So each cell in this 80 volt 33ah pack is contributing 1/3rd of an amp.
Line 7 = Line 10, and would for any battery chemistry and arrangement where the voltage is halved and the paralleled-cell capacity is doubled (meaning total energy available for the entire pack is constant).