So they were never secret in the first place.
I have never understood the desire to have voting machines when a paper ballot works just fine. We tried electronic voting in three municipal elections in 2008 and courts ended up invalidating the results due to horrible usability issues.
Incredibly resistant to influencing at scale, resistant to voter coercion, transparent, and invokes a sense of occasion and community spirit.
The problem with electronic systems is the public can't see the piles of votes, can't get involved in the count, and ultimately it's the perfect system for being able to tip the scales subtly.
Even vote counting machines for paper ballots are a mistake in my view.
The need to balance voter security, with auditability, rapid Ness of results, with ease of setup/teardown of the voting place, is hard to beat with scanners.
(Within reasonable limits, I mean.)
There are elections in India and the US to control billions of people and some very aggressive military people armed with weapons capable of ending modern civilisation. This is one of the most fundamental social technologies we have to keep the whole system stable (up there with limited liability corporations and courts). The downside of one of those elections failing because of voting machine trickery is stupendous.
Frankly, I'm not sure even auditability is that important as a design goal compared to voter security. If the election is close enough that an audit matters the two candidates are pretty similar. In practice, if there is any meaningful gap in preferences then the outcome of the election should be clear enough that an audit isn't that meaningful. It's nice to have and it is cheap enough to include in a paper ballot.
Because it is a low-frequency, high-importance activity that uses public facilities.
We close the polls at 1900 and have a Collector Officer run one copy of the data on a thumb drive to the County.
The Chief gets to deliver a backup a couple hours later.
Hand-counting the ballots instead of scanning would be expensive in terms of time and money, and error-prone.
I'd argue that Fairfax County, VA is about optimal, all factors considered.
As I'm fond of saying: "Virginia is for lovers...of elections."
In Blighty, we have paper voting. The polls close at 10pm, the manual count takes place overnight, and the result is typically known the next day.
How much more rapid do you need?
In the US, the election is in November and the president doesn't get sworn in until January. It could take a couple of weeks to count the votes and it would be fine.
Unless those volunteers are all die-hard fans of a particular party/candidate and thereby intimidating everybody that has a different opinion. (Not openly of course, but if everybody knows everybody, the mere presence suffices to sway people.)
The process is quite fair and rigorous.
I think machines are only acceptable if they sort ballots into multiple bins, not if you are using them for the actual count. The bins should be designed so you can casually see that the last ballot to be added is correct for that bin while the machine is working. Something to insert a marker every 100 ballots is probably a good idea, then you can count the number of hundreds, and randomly sample a few of them to check they are correct.
This is the right answer. Using tech as an auditor for batches after manually counting could be useful. Getting everyone together to count votes in a process that everyone can see, understand, and be personally invested in - that process is what is needed far more than efficiency, at this point in time.
In person paper voting, however, only works on a relatively healthy democractic community. What used to happen around here was that whoever was the local hegemonic power, mostly oligarcs, sometimes gangs, would just plant a grunt in the voting halls and coerce people to reveal their votes. That or they would simply have a bag of pre-cast votes and drop them all in the ballot box. Lots of absentees and dead people used to happily cast votes at the time.
So ultimately the full electronic system has been working quite well over here for the past 30-something years. It has only really started to be aggressively questioned since 2016 with the rise of social-media as an election driving powerhouse.
For example, while the software and hardware is audited by a very diverse panel, it's too institutional: you can't inspect it as an independent researcher. It's also not clear which parts of the supply chain are subject to the audits. I trust it's all of them, and these institutions are doing their job of pointing out the parts that they have _not_ audited, but I, as a member of the public, can't verify.
Some states do quite the opposite, e.g. seal ballots after the election and only allow inspection by court order. This has obvious benefits for secrecy, but then creates a lot of objections when people/organizations that doubt the election outcome are told that they cannot review the actual ballots (without meeting some threshold to justify such an order, which can be quite high since these rules were often put in place to try to counter pay-to-vote or voter intimidation schemes).
The existence of such a ledger isn't even required, but it makes it radically easier to audit the count process to detect errors. US election administrators demand a very high level of accuracy in vote counts (higher than what is typical in a lot of other countries), so in hand-count processes it's common to tabulate each ballot multiple times, and with machine tabulation there is usually some kind of automatic recount or risk limiting audit, either by retabulating with separate machines or hand-counting a sample. All of these are much easier processes when you can correlate a ballot to the previous time it was counted, so that errors discovered in auditing can be tracked to the specific ballot that was miscounted and corrected. Otherwise, if you count a batch of ballots twice and get different results (which is virtually guaranteed with hand counting), you will have to recount the entire batch over and over until you get satisfactory convergence. There are several different methods of doing this: some jurisdictions serialize ballots when they are printed so that tabulation can be tracked by that serial number. Other jurisdictions avoid this potential secrecy hazard by only serializing ballots after initial tabulation (e.g. ballots pulled for a sample audit have sequence numbers added on stickers or hand-written). Some tabulating machines can add sequence numbers as they run. All of these have different considerations as far as reliability and secrecy, but unfortunately there is next to zero funding or political interest in researching these issues and applying the resulting knowledge. The result is that everything is highly variable from state to state and some states continue to use processes that are known to have significant defects, most famously Louisiana with its ongoing use of non-auditable DRE machines (the only state that continues to do so).