From what I recall, our polling station, which served only a small portion of the city, was broken into several polls, each run by 2 or 3 poll workers.
At then end of the day the poll workers personally counted the ballots they collected at their poll (so every ballot was counted at least twice, and each individual only counted a fraction of the ballots at the station.) Monitors from the different political parties were free to watch the whole process.
I'm definitely getting some details wrong, but generally the whole thing, plus automatic recounts for tight races left no doubts for me.
The US has indeed largely moved towards "voting machines," but I should be explicit about what this means. These aren't the touchscreen computer-only (direct-recording electronic) machines that were hastily deployed after Bush v Gore. The overwhelming majority of states and municipalities now use some kind of optical-scan paper ballot technology, like scantron forms that are tabulated and kept safe in a box with a scanner bolted onto it. So even if the scanner is broken, there's a reliable record of voter intent.
https://ballotpedia.org/Voting_methods_and_equipment_by_stat...
Results don't take long to count, even though there are about 30 million ballots. Polls close at 10pm, the first constituency declares some time between 11 and midnight usually, it's 90% done by about 6am[1], and the last will be some time on the second day if there are multiple recounts. Due to the FPTP system, it doesn't really even matter about the rest once the post is already reached - which is its own problem, but it's not like machine-based recount drama doesn't drag on for ages too.
[1]: https://researchbriefings.files.parliament.uk/documents/CBP-...
We should also not be accepting votes with date stamps past election day. Or votes with no date stamp.
If we go all-in on electronic ballots, I think this is the place we could use a block chain to ensure security, traceability and accountability.
In fact voting is extremely accurate throughout the democratic world regardless of counting method, and this fact wasn't particularly controversial for decades and decades.
The idea that we somehow have a problem to be solved is the actual attack on democracy. And it's working. I know it sounds like hyperbole, but there is a very serious risk that the USA has already seen its last peaceful democratic handover of power. The people with control of the levers of power seem extremely disinclined to accept loss of that power.
Voting machines are far easier to hack than human processes, and there have been numerous presentations on this particular topic.
American politics being off the deep end is an entirely different topic.
Voting machines are have proven to be reliable in the US. Dominion Voting continues to rack up huge defamation wins in court over this. You're just FUDding.
Money doesn't work like ballots. All ballots are the same value, and each voter is entitled to one only.
If the pennies in my account are miscounted, I certainly won't give a damn.
I think America leaned too far in on the voting machines, TBH.