Another possible factor is that US elections generally see far more races on the ballot. In my ballot this year, I had to vote for US President, US House, US Senate, State House, State Senate, Councillor, Register of Probate, and three referendums. That's actually a pretty light ballot; in the past, I've also had to vote for races such as County Auditor, Recorder of Deeds, County Clerk, Soil & Water Conservation District Commissioner.

It obviously takes far longer to count ballots by hand when you're dealing with a dozen races instead of one or two.

Actually most places I'm aware of count paper ballots. Germany, Sweden, Australia all use paper ballots as far as I'm aware (unless something changed recently) and in all of the countries results are typically in during the night of the election. And many of these countries have also significant option in their votes, I mean Australia's preferential system means you have a lot of choices (if not going with the party preferences).

I think one reason for the US system to be this complex is essentially corruption, i.e. funnelling money to the makers of voting machines. The other reason is that the US system highly encourages parties to try to get votes of the other party discounted based on technicalities.

It still boggles my mind that in the US, the first modern democracy the system developed to discourage voter participation

My ballot had 35 positions to vote on.

I sometimes wish we had a separate federal / state / county / town vote to keep the practice up and reduce the overhead of individual voting periods.

It isn’t unless you have valid mail in ballots that haven’t even arrived by Election Day.

17 million votes don’t take as long to count as 175 million?

Why not? Larger countries have more places voting happens and more people counting. It parallelizes almost perfectly. Slow counting is almost entirely down to resource allocation.