I agree that you could easily design a system where you could have video of everyone dropping their ballots into a ballot box and it would still be impossible to associate a particular vote with a voter.

However, that's not the standard. The standard is avoiding the appearance of being able to track votes. I don't trust the people who make voting machine software or the government. You don't know that your voting tabulation software correctly anonymizes the results and you shouldn't need that technical knowledge to feel safe. The correct approach is to make a system that guarantees what we want and would be impossible for a bad actor to abuse.