You are misrepresenting the checks in the paper system. There are representatives of all major parties and the state at the voting station. The representatives

You are misrepresenting the checks in the paper system. There are representatives of all major parties and the state at the voting station. The representatives have competing interests, so you can trust that they won't collude. Plus the state rep has a legal responsibility to ensure there is no cheating. You put the piece of paper in a locked box - a lock that was checked by all these reps. So, no wrong votes in the box. At the end of the day, all party reps watch as the state rep counts the votes. So the counting is also right. Then the counts are written on a final document, which is then signed by the state reps and party reps. At the main station, more party reps can check that all papers were collected and correctly added for the final tally. Anyone who wants to mess with the voting has to corrupt all of these reps for a voting station, in order to probably move the votes by like <1%. Then repeat for many different voting stations to actually change the winner. As long as you trust the local party rep (hopefully you have interacted them) who is standing at the voting booth, you can believe at the emotional level that your voting booth got the right result.