> Why can't I apply this logic to current election systems? You can memorize and regurgitate a usa.gov or National Archives article to articulate it - but 95% of the populace doesn't actually know about those ballot counts, ballot transportation, result tallying, transmission and communication of said results, implications of Independent State Legislature Theory and how challenging it - at least on originalist grounds - can cause 50 different processes for each of the 50 different states, etc etc etc.
The paper voting system is extremely simple, it takes maybe an hour or two at most to explain in any detail you want to anyone who wants to understand it. People can, and many do, register to participate and see it working first hand. The US presidential election system is slightly more complex because of its legal nature, but I am discussing paper based voting in general; and all of the legal complexity would persist even if each state moved to a blockchain or digital based voting system.
In contrast, understanding zero-knowledge proofs requires college-level mathematics knowledge, probably requiring some months or even years to teach to someone who works in a non-mathematical domain, and at least a day or two to really get it even for someone with enough math knowledge who hasn't seen it before. And this is only the theory - the practical parts are in fact MUCH MUCH more complex - to the point that it is almost certain that there isn't a single person in the whole world who could actually confirm for himself that an electronic voting system actually implements the algorithms promised. Establishing that a CPU is executing the code you think it is is extraordinarily difficult, and doing so for the many such systems that would compose an electronic voting system is way past any human.