Voting is the way it is specifically to combat this problem. Your solution tries to fight against a problem that is basically impossible without systematic widespread corruption by opening it up to localized corruption which is historically common. You're solution doesn't make the situation better it makes it worse.
Anyhow if you can't understand why secret ballots exist after all that explanation I'm never going to be able to explain it in a way you understand so I think we're done here.
Our current voting system IS secret ballot, and IS also ALREADY based on computer DATABASES (not paper). You fail to realize that blockchain is basically just an encryption strategy for databases. It IMPROVES database security. It has absolutely nothing to do with whether votes are kept secret or not. It ONLY has to do with whether it's technically possible to tamper with the data or not.
Bottom line is: paper ballots CAN be tampered with (whether secret or public) but blockchain cannot. Got it now?
Anyhow if you can't understand why secret ballots exist after all that explanation I'm never going to be able to explain it in a way you understand so I think we're done here.