This problem might have a technical solution though. First, each voter generates a private key and publishes the corresponding public key. Then implement a homomorphic vector addition, everybody submits their vote as an encrypted vector, and then you somehow add the vectors together homomorphically, i.e. the addition can be done without decrypting them first.
You need some kind of way to prove that each vector corresponds to a legal vote (i.e. increases the vote total of at most one candidate by at most one vote.) Then you need some way to decrypt the encrypted vector sum using some amalgamation of everybody's public keys, but without allowing to decrypt subtotals for particular subsets.
You can publish all the encrypted votes received and the decrypting amalgamation, so anyone with the capability to download and process a large data set. Anyone can check that every vote was cryptographically approved by a distinct pre-registered voter and the votes were totaled honestly.
If we assume an upper bound of 1 billion voters, each 1 kb of encrypted vector size adds 1 TB to the raw vote data. Based on existing "clever" cryptosystems that do similar things (e.g. ZK-snarks), it's reasonable to guess we won't need more than 100 kb per encrypted vector. So an entire 1-billion-voter election could be processed by a small storage cluster with 100 TB, you can't verify it on your laptop, but the technically inclined could verify the vote themselves for probably somewhere around $1,000 - $20,000 of hardware and sysadmin time.
I don't know if there's existing crypto math to do this, but I'm pretty sure it at least hasn't been proven impossible.
The kind of crypto primitives needed for this kind of system might be found someday.
The problem with verifiable voting is that it has to break one the properties of American democracy, the secret ballot, or else it doesn't really work. As a voter, I want to see that a) it was recorded that I voted, and b) what my vote was. In the case of invented voter fraud, both A and B need to be possible, but making both of those possible mean it's possible to show who I voted for. Who I voted for is a secret, and is one of the central tenants to American democracy. I can talk about supporting candidate A in public and vote for candidate B in private and a lot of properties follow from that.
The challenge isn't technical, it's a social problem, and technical measures won't solve social problems.