I realize state of the art, modern, high-performance systems are incredibly complex... but that doesn't mean all systems have to be incredibly complex.
Simple computerized systems are incredibly accurate and reliable, easily moreso than humans.
And critically, it's feasible to perform attestation on electronic systems: something that's completely impossible with humans. You have no idea if Joe or Sally are randomly slipping in a few miscounts (or the people auditing them, or the people auditing them). If you're careful, you can be sure that only specific code is executing.
I'd be fascinated to get a breakdown of trust in computerized voting systems, from programming professionals, by programming speciality. I have a suspicion you'd get different answers from firmware/RT folks vs js front-end, to pick a couple of examples.
Such systems are better enough that businesses handling cash use them to count paper money.
Next to voting, or perhaps ahead of it, people surely value reliable accuracy in their money. So why not ballots?
Sure, we use a computer to produce a paper ballot (computers DON'T count or keep counts). The voter has a voting id that is hashed/encrypted/processed in such a way that the number is verifiable as a valid ballot hash (maybe using some sort of public/private key pair) so hashes can't simply be randomly generated.
So the computer UI produces the ballot. The voter is told to check their ballot reflects what they wanted to vote for. The ballot is scanned with a scantron.
pretty easy if your company produced the machines
I know a guy who did this for a job for a company that produced food
https://en.wikipedia.org/wiki/Estimated_sign
his entire job was to allow the company to push up as close to that line as possible without going over when checked randomly
saving them tens of millions a year
Teachers and students understand how this all works, so it has a lot of trust.