Should the American voting system run on blockchain?

Ideally yes except for what I consider to be one huge problem. If the blockchain is public and voters names can be associated with votes then it's a bad idea. The American voting system is based on the secret ballot. Who I vote for in a political election is my business and nobody else's. If someone can deduce from data mining the blockchain how to associate a voter's identity to their vote then the data miner can look back on the blockchain and get an entire history of how I or someone else has voted in the past and I consider that an invasion of privacy.