> If we can have a secure and audit-able banking system (and every other aspect of our lifes), surely we can have the same for voting?

There's one major requirement in voting systems that throws a huge wrench in everything, anonymity. In order to prevent vote buying and coercion voters can't be tied to specific votes. So any system that allows a person to check that their vote got counted for their candidate isn't workable because that violates the anonymity requirement.

There's a million reasons that votes change as they're counted and recounted. For one in some states absentee ballots can be postmarked up to the day of the election so they can trickle in for a while after the day of. Another is machine breakdowns and just mistakes as the complete numbers are gathered.