I think the discrepancy here are that there are very specific types of trust we want to discourage in voting: specifically, trust between bad actors or between bad actors and potential victims.

The secret ballot, by definition, just requires that no one except the voter can possibly know who they voted. It doesn't prevent coercion for party registration or PAC funding - those are separate issues which have their own ins and outs.

You argue in favor of a private - not secret - ballot. I hear you and understand the value you find in that. It would be great for cases when there are no bad actors AND when people don't trust their votes are being counted accurately.

However, a private ballot like you endorse is completely open to coercion and corruption, even with read-only access. Imagine that a random person honestly offered to refund me for a debit card purchase of $20 at Wal-Mart. In the private world you're describing, Wal-Mart, my bank, and I know that I did. However, I can still validate it by showing the random person my private bank account statement.

In the current, secret ballot system we have, no one would rationally offer money for my vote because there is no legal way of validating the transaction. Even if I do as they wish, they have no way of knowing that I'm not lying through my teeth. In your private ballot system, I can use my read-only access to show the candidate, a party leader, my boss, or landlord that I completed my end of the bargain. Now, they can establish trust: they can use my ability to access that data to confirm that I voted the way they wished. As a result, they can coerce or bribe you or I to vote the way they wish.

We need a secret ballot because anything else opens the gates to corruption: your employer or landlord would coerce you to vote a certain way, or people would sell their votes. Those are the reasons we moved to a secret ballot in the first place.