[rtkwe]

So there's a couple thing to unravel here. First, each county in the US runs their elections separately so within a single state you might see a couple different systems. Some places like my area in North Carolina use a system like what you describe except the ballots are scanned through an optical scanner then stored in case there's the need to do a recount. There's no central board above the county level that the ballots would be sent to for counting.

Second electronic machines are popular because they speed the election counting and are cheaper to run because the election board doesn't have to print tens to hundreds of thousands of ballots. A good electronic voting machine reports the vote 2 ways digitally to some vote tabulator local to that voting place and with a paper record that can be audited. The paper print out their having printed in this video is the end of the night tally that'll be reported to the county/state board of elections to be combined with the rest of the results.

Third doing it on a centrally located machine instead of over the internet adds a lot of security to the process. Trying to properly secure single purpose hardware like a voting machine that can be kept in a monitored location is a much simpler task than trying to find a way to ensure the Joe/Jane Voter's computer isn't compromised when sending the data to their counties board of elections. Not to mention that by accepting votes over the internet you're opening yourself up to everyone being able to remotely attempt to exploit the system. At least with a voting machine only connected to other election hardware attacks are limited to someone that's physically at the voting location. It's also tricky to prevent double voting while maintaining complete anonymity.