Existing voting systems do have a countermeasure, if not a fantastic one: creating a trail of physical artifacts that can be manually audited to verify vote totals, and a roll of accepted votes to compare the count of said physical artifacts against. It's not fantastic because the error rates on those physical artifacts are stupendous, but tampering with votes at scale can then require (a) physical access, which humans are well-equipped to reason about, and (b) generating and destroying big piles of said physical artifact, which is expensive and expensive to hide. The gold standard of tampering with physical elections that we know of is basically denying observers the chance to audit, which is rightly considered suspicious.
Tampering with electronic votes at scale does not have these cost properties. We can magnify costs without giving voters the ability to prove their votes to a third party (I am aware there are probabilistic constructions), but all such constructions (a) are much harder for the average voter to reason about than monitoring physical access (humans are quite optimized for monitoring physical access), yet (b) requires voters to actually audit their own votes and report non-inclusion en masse. You can see why this is a non-starter.
So the common person will probably not understand the cryptographic underlayers of this theoretical new system, they need to have confidence "in the science". I know that doesn't sound as good, but we're heading towards a world where computing literacy is increasing, so in some years that could be possible.
The problem of unscrupulous operators can be circumvented if the votes are in a public ledger where the voter can backtrack their vote to the ledger "yes, its' my vote, nobody tempered with it", but the vote in the ledger can not be linked to the voter.