And it quickly becomes unmaintenable, "three can keep a secret, if two of them are dead".
Making a conspiracy like that work at US scale would require a small country's worth of conspirators which really, really wouldn't be able to hide from the light of day for very long.
To hack the U.S 2016 votes you'd only need to flip a few counties in Pennsylvania, Michigan, and Fl.
It would take an immense amount of reorganization of trust, but open hardware verifiable (both in person and on some kind of trustless ledger akin to a blockchain) voting systems would be more secure against such national actors, because there would be no back room to burn the paper in. If the machine is public and you can trust it, and you can trace the results nationally to insure the results were accurate, you have more security than you have now.
True, but it is significantly (as in several orders of magnitude) harder to hack paper at a national scale than it is to hack an electronic voting record at a national scale.
Hacking paper requires people physically interacting with that paper to subvert it. That amounts to 1+ person per box of paper votes.
Electronics just needs the one person who discovered and exploited the vulnerability.