The entire point of a recount is that when the votes are close enough to swing the balance of an election, they're recounted, potentially repeatedly until we can be sure they're correct. They're essentially never more than a few votes off either way. If it's not close enough to swing the balance of the election, it doesn't
really matter that a dozen votes were miscounted - we'd prefer that not to be the case, obviously, but not by breaking the other properties of the system.
Short of some very very clever cryptography, you really, really don't want to be able to verify your individual vote, because that means you can verify it to others - the entire point of this process is to avoid coercion, or else there's much simpler solutions. (Pull everyone into the polling station at once and have a show of hands, for example.) You want to verify that one ballot was given to each person registered to vote, and that all votes were counted correctly, but you don't want to verify that an individual person's vote was counted correctly.
