The secret ballot appears to be a security trade-off, but isn’t: public ballots don’t provide additional security. People at times call for public ballots to provide some perceived verifiability which only ballot traceability can provide.
The secret ballot requires that a person cannot prove—even by their intent—that any given ballot is their ballot. Once a person can prove how they voted, someone can coerce the voter into voting a particular way with threats, bribes, or social pressure.
Public ballots allow an individual to validate their own ballot, but not every other ballot. Any individual may notice their ballot has changed and call out the Board of Elections—assuming the voter isn’t lying because they dislike the outcome, or simply misremembering how they voted. If you can buy a bloc of dishonest voters, why not buy a bloc of dishonest vote protesters?
Our anonymous ballots protects us from a great degree of election tampering, without which we could not vote honestly. While public ballots theoretically allow any voter to call out an incorrectly-recorded vote, a voter could lie, making public ballots a worthless security measure.