Right, we’re not dealing with banks here. Ultimately we’re picking between N alternatives. The size of the gap between them doesn’t really matter, as long as it preserves the correct ordering of winners. Given that, using statistics to reduce your work is a completely reasonable efficiency here.

Ballots can be kept track of, just like dollar bills can be. It's not rocket science.

This is a terrific idea.

For voting in the USA to be like banking, with matching credits and debits, some changes must first be made.

Every eligible voter must be issued a ballot. Prerequisite is automatic universal voter registration.

Every ballot must be fully marked. No under votes.

Every issued ballot must be cast. aka Compulsory voting.

You have my full support for your "voting like banking" reform.

I like double-entry bookkeeping as much as the next guy. But your proposal isn't double-entry (which requires every ledger entry to net out to zero), it's more akin to aerospace/NASA style reduntant control systems where you have independent implementations that must agree with each other for their output to be propagated.

Redundant control is a great system if you need to provide realtime output with high correctness requirements (though for this of course three implementations is better than two as you can discard one faulty output and continue with the quorum output).

In elections, we don't need to provide real-time control; in the happy path the random audits don't add an unreasonable delay, and when they do find a discrepancy we're fine to wait a week or two if needed for a full hand count.

Another reason why banking/accounting is a poor analogy: in banking, you don't have anonymity requirements. Each transaction is tied out to a known individual (even more granular than that really); you can do double-entry bookkeeping because you know which accounts to debit and credit for each transaction, and maintain the accounting invariant that all accounts sum to zero. In voting, we have strict anonymity requirements, so there's no equivalent "debit Alice's account of a vote, and credit Candidate Bob's account" operation, and there is no equivalent to "netting the voting accounts to zero" that I can see.

Another way of thinking about this is the RLA is simply a different approach to provide your second implementation of a vote tallying machine. It's an implementation that uses manual (human) counting, and for pragmatic cost/time reasons doesn't count every vote, just enough votes to get statistical confidence that the result is correct. And, if you have two machine implementations, who's to say that everyone will trust one of them? You still need to solve "trusting trust" for each one, and while it's harder to subvert two systems, there's no reason it's impossible. Whereas I think it's a lot easier to produce a human-powered vote counting system that is transparent and trustable by virtue of its simplicity.

Down the road I'd be happy to put a second vote tallying machine in place to provide better assurance of the initial counts (and I'd love to stop using closed-source private implementations), but I think it's important to be pragmatic here and focus on the best ROI steps, and I think implementing RLAs and abolishing DREs are two of the very-high ROI items we should be focusing on first. Adding RLAs to all states would be a much better improvement than adding a second open-source machine tabulator to all states.