It doesn't have to involve something adversarial like theft - a bigger risk than coercion is explicit bribery. If you can prove that you voted for something, then you can prove your vote in exchange for a bribe.
The reason every functioning democracy uses a secret ballot is that coercion and bribery were trivial wherever the ballot wasn't secret. Bribery might sound uneconomical for a national election, but there will be plenty of local elections using the same machines where it could easily make the difference.
People taking bribes to vote a specific way are already likely trying to cheat the election for bribes. You're talking about people that are on meth that will do just about anything for money. If all else they could have a sting where the police says they'll give them triple the money if they narc and then arrest them for selling their votes and others for paying for vote manipulation.
The reason every functioning democracy uses a secret ballot is that coercion and bribery were trivial wherever the ballot wasn't secret. Bribery might sound uneconomical for a national election, but there will be plenty of local elections using the same machines where it could easily make the difference.