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