1. verify who is voting
2. verify trail from voter to count
3. no extra votes
4. no discarded votes
As the recent US elections showed, voting machines are open to the opposition saying "we only lost because the machines were hacked against us".
This is naive. The Georgia Presidential election was hand-recounted, twice. The loser still claims it was stolen, incited an insurrection that sacked the Capitol while Congress was certifying the winner.
When one party is solely dedicated to power, not democracy, none of your ideals or safeguards mean anything. They just don't care what anyone thinks as long as they can hold power.
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