That is why paper balloting is such a durable voting mechanism. Pretty well anyone can understand how you would take a stack of paper ballots and decide who got the most votes. From there you just need to maintain a chain of custody where all ballots are monitored by any interested parties from the time they are cast to the time they are counted.
The more technical you get with your voting solutions, the less overall trust the public will have in the final vote counts.
In the 2020 presidential election, tens of millions of people had trouble understanding how paper ballots worked. I'm not sure the argument about public trust is that durable or cogent at this point.
If we created a cryptographic voting system with homomorphic encryption to preserve privacy, they would be claiming the exact same thing — except in that case, you wouldn't be able to recount the ballots by hand.
If you allow physical voting places, then just make a machine that gives a paper recipt and do risk limiting audits. Problem solved.
Personally i think risk limiting audits of the original physical documents is a much more secure system.
1) Votes must be private and anonymous (i.e. not linked to your identity)
2) Voting must be secure
It's easy to satisfy either one of these requirements, but currently impossible to satisfy both.
A secure vote is one that has a result that cannot be altered once it has been cast.