Sorry can't reply to your reply but... Making the ballot a zk-SNARK[0] would allow it to be queried for validity of certain assertions like "Did this ballot contain a vote for Candidate A or Proposition B" without leaking the identity of the voter. The voter's private key could decrypt the entire ballot perhaps for the voter's verification or even as another verifiable assertion that the ballot was signed with the specific key. Perhaps there would be a key provided by the voting authority body as another verifiable assertion that would allow the voting authority body to verify the user for their purposes if required.

I agree that the more difficult part of this would be encouraging adoption and supporting use. There are hardware keys like yubikeys or hardware crypto wallets that can be populated with voter-generated keys to be used in the voting process, and these hardware keys could be populated in a process similar to getting a driver's license perhaps, except not waiting for it to arrive in the mail. Perhaps you go into your local clerk's office and they have a one-time key generator that populates your hardware key. I definitely haven't fleshed this idea out beyond some basic musings.

[0]https://z.cash/technology/zksnarks/

Sorry, I'm not well versed enough in zk-SNARK, can you explain how it solves the problems above?

If it does do you think that you can make the general public trust/understand it enough to run a election?