"Which mods, specifically, preclude the capacitor from being able to do that and why?"
My first thought was the electric starter! But, of course you could still kick or, in my case, bump start the bike (I removed the kickstart lever a couple of years after installing the Alton E start). However, re the Cap - my own experience was that the cap could not start the bike with an EI/Podtronics. So I removed the cap when I installed a new wiring harness years ago. Whether it was the Boyer or the PodT (or both) that precluded the cap from starting the bike, I don't know. But I could not kick start the bike on just the cap.
Further, I can see no point in the cap, even if it will start the bike. There is a battery and a charging system. Certainly, in the days of motos with marginal DC generators and tiny batteries, there was a logical reason for the cap. Batteries were often flat. Nowadays, it would require some pretty dedicated lack of attention/maintenance of the battery/charging system to make the cap necessary.
OTOH, there is certainly no need to remove the Cap except, as the OP observed, it takes up some space. As far as whether it will actually (kick) start the OPs bike in the configuration it is in, it's easy enough to test. Disconnect the battery and try to start it!