I think blockchain as a chain of custody tracker (rather than a vote tallier) for ballots might work. Could be used to track printing, delivery to a polling place, it being filled in and returned to the poll workers, and all the steps along the way to it being actually counted.

The main failure mode of paper ballots is they seem to be "misplaced", or out of the blue some box of ballots no one seems to remember appears. This would make that harder to do and is about as much as I'd trust a software system to do correctly.