As others have said, the scalability ideal is to have electric/mechanical counters but with paper ballots. Keeps the paper trail for double checking, but also allows poll workers to deliver quick initial results to everyone breathing down their necks.
Pretty sure that's how we do it up on Canada. I think random samples are hand-counted to make sure the machine count is accurate. There's early voting too so not all just in one day.
That's how we do it in my part of the US. And the whole thing is live streamed and audited. My mail ballot is also scanned twice, and I can check if it was received (and signature checks out) and counted. If there's an issue, I can correct my ballot before election day.
Well here in Germany we have about 40-50 million votes to count in a federal election. Right when the booths close we get an exit poll that is already pretty close. After 1-2 hours there are extrapolations that are even closer and next morning, there is usually the certified result. All on paper, counted by hand.