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Public voting history would make elections undeniable. The obvious issues are coercion and persecution, but would these problems be at a scale that would meaningfully interfere?
1Voting in America used to be extremely public (up until the late 19th - early 20th century) and I believe the general consensus among historians was that the benefits massively outweighed the harms, see this article for an in depth analysis. It's possible to argue that the biggest problems (blatant coercion both positive and negative, direct persecution, fear tactics by employers, etc) might be alleviated by the modern context, eg it would be nigh impossible to cover up blatant bribery or coercion with the existence of the Internet and cell phone cameras, but my belief is that the potential problems still massively outweigh the potential benefits. Fear of retribution or consequence should never be a factor in voting in a functioning democracy, and it feels obvious that there would be social consequences at the very least! Think someone losing a friendship because of their vote for Trump in the 2024 election, or a woman in a deep red state being scared of emotional or physical retribution by her husband for voting Democrat.