Imagine a world where cryptography doesn’t exist, so we have to trust volunteers to hand-count easily-forged pieces of paper.
Cryptographic software is tricky, very easy to implement incorrectly or with major security gaps, completely opaque to the amateur user, vulnerable to all kinds of zero-days and possibly even progress in mathematics (God save us from the day when someone comes with a fast factorization algorithm). If secure enough, it will be burdensome enough that people will try to circumvent it. It runs on a stack of OSes and hardware that may (read: of course they do) have fatal security flaws rendering your secure app insecure.
No, thanks. Give me a paper ballot any day.
Protocol: Alice and Bob send their votes to Eve. Eve wins. The end.
What IS easily forged and extremely difficult, if not impossible, to secure is a result printed out by some opaque computer that is running a huge amount of software on an extremely complex processor which runs its own closed-source firmware, probably communicating over the internet 'securely' to some other computers.
The manager rounds up the workers and "suggests" they all compare how they voted. Those who voted "pro-company" will likely reveal their vote. So for everyone who refuses to reveal their vote, the manager checks a box next to their name on the attendance sheet.
There may be a voting system that provides all the desired guarantees, but I doubt such a system is also easily understood and trusted by the average voter.