Sure, it's a good system.
But, of course, if you had a camera, voters might reasonably be worried that you would combine the footage with vote order and figure our who voted when.
But, of course, if you had a camera, voters might reasonably be worried that you would combine the footage with vote order and figure our who voted when.
This doesn't seem hard at all to do right.
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.
Any gaps in that leads to suspicion of error and fraud. That leads to bad things, as recent events amply illustrated.
Yes, it can be done while still having a secret ballot.
No such system is possible