Exactly. If chain of custody is broken, it's not in the pile. People from all sides of the electorate should be able to observe every box at all times if they wish to follow it.

Mail in voting is similarly exceptionally easy to game. Oops, lost 1% of that zip code... bummer...

Imagine a very large mostly volunteer-run event that only runs once a year or so and where some fraction of the volunteers are running the event for the first time.

At the end of the day all the important equipment gets packed up, shipped somewhere, and unpacked.

But sometimes -- rarely, but sometimes -- some really important piece of equipment gets left behind at the event site or unpacked incorrectly at its new location.

I just described marathons, carnivals, and... voting.

In Germany, we also have paper based voting and yet, we do not have the issue that ballot boxes disappear. Everything and I mean literally everything is accounted for and if the numbers do not match up (e.g. less boxes of ballot boxes than before, or n(valid votes)+n(invalid votes)!=n(total votes) there is an immediate recount. No one leaves until shit is done, and if it gets too late everything is packed up, sealed and boxes counted.

The horror stories of the US are a failure of their system, not of paper voting.

Each voting machine could tally the number of votes but not the vote itself. The count is encrypted and only the governor has the key.