No, because they have no idea what your true ballot ID was.
They can force you to show them a ballot, the idea is that all ballot ID's get made public. You could be showing them anybody's and they'll never have any way of knowing.
It seems you mean something simailar to Selene voting system where a tally board is published containing tracker vote pairs. Each voter can decrypt their tracker once the voting phase closes to check the vote and also means to fake the decryption for claiming another other tracker from the tally board as yours.
Not necessarily. In Colorado they handle this by putting the ballot in a blind envelope inside a trackable envelope. I can verify the details of the receipt of that trackable envelope to the tallying center where it is verified as untampered and opened under video with multiple people present. The unmarked envelope is added to all the rest of the ballots to be counted.
So then you can verify your vote reached the tallying center, but not that it was tallied correctly. Someone can look at your vote and count it wrong.
I think that's fine and the best we can do, but the person I replied to said you can verify your vote is tallied correctly. That implies checking what the actual vote was.
All true, but this is no different than any other ballot in the state. At a certain point you can choose anonymous ballots or you can choose trackable ballots.
Receipt-freeness (i.e., a secret ballot) is usually the desired property. Yes, a lot of people like you state they desire verifiable votes. But that's where you need to respond to the points the person above you is making: how is such a system not also susceptible to coercion and bribery?
(However you would verify your vote, imagine the person who is coercing you is just standing over your shoulder with threat of force. An example might be an abusive husband who does not want to allow their wife to vote freely/against him. A briber might simply force you to allow them to look over your shoulder before they'll pay you off.)
Vs. paper ballots in a polling place: a coercer would not be permitted in the poll booth with me. I get to vote, and when I leave, … I can tell them whatever, but it does not need to match my vote. It utterly defeats bribery, as the briber has no way to verify that I'm doing what they way.