It’s far harder to achieve mass manipulation of the ballot when it’s all being handled by a lot of human hands. If it’s managed by computers, then by finding a bug or other vulnerability in the software or database you could alter the whole election.

Meanwhile, to manipulate a paper ballot & hand-counted election in the same way you’d need the cooperation of a huge number of people, and you’d need them all to keep their mouths shut. That’s far more difficult than defeating a computerised system

X^0 and 0! aren’t actually special cases though, you can reach them logically from things which are obvious.

For X^0: you can get from X^(n) to X^(n-1) by dividing by X. That works for all n, so we can say for example that 2³ is 2⁴/2, which is 16/2 which is 8. Similarly, 2¹/2 is 2⁰, but it’s also obviously 1.

The argument for 0! is basically the same. 3! is 1x2x3, and to go to 2! you divide it by 3. You can go from 1! to 0! by dividing 1 by 1.

In both cases the only thing which is special about 1 is that any number divided by itself is 1, just like any number subtracted from itself is 0