The problem is much simpler. If people could verify if their votes were counted correctly, at least 1 out of 20,000 would claim that their vote was counted incorrectly while it wasn't. Some are malicious, some pushed the wrong button, some just forgot that they changed their opinion since then.
That would be a very vocal minority that would immediately destroy any trust in the system.
That would be a very vocal minority that would immediately destroy any trust in the system.