"We want you to vote for Jim Totes-Legitimate for President. But so that we can recognize your ballot paper and we can verify that you voted for him and we don't have to break your kneecaps, please also mark your other ballot races as follows: Fred Also-Ran for First Assistant Flangedoodle, Sheila Plausible for Second Assistant Flangedoodle, Hazel Placeholder for Junior Hog Counsellor."
Not hard if you've got 10 or so multi-way contests or 20 or so ballot measures.
Which is also why the cryptographic voting systems cannot protect voter privacy. Those systems require hash collisions to hide your ballot in the herd of ballots. But the combination of precinct size and complicated ballots means any particular ballot is utterly unique (no hash collision).
I'd be far more charitable towards crypto advocates if they also specified the conditions required for their system to work correctly.
Similarly, with postal balloting (vote by mail), your ballot is batched (upon receipt), so will be mixed with ballots from other precincts, therefore more easily tied back to its voter.