The media used for voting doesn’t matter if trust is questioned. No single individual is able to count all paper votes either, so it’s fundamentally about citizens trusting authority.
Also, some states use electronic voting/counting machines, which should be looked at with suspicion. How can you, as somebody who wants to verify the integrity of an election, observe that they are not subject to vote manipulation?
Paper voting has the same central point of failure as the above proposal, they effectively have a voting pool manager, which is the State itself (though different in each State). These are notoriously bad at managing the voter pool, and issue ballots for the dead and people who have long emigrated. There are issues with people who have moves states and are issued ballots in multiple states - under mail-in voting they can trivially vote twice. If they were forced to vote in person they would have to make the trip between states on voting day.
> No single individual is able to count all paper votes either
Compare "I can't count them all myself but I can see and understand the way it works" with "I can't count them myself and I can't even understand how the system and validation work".
Imagine if trump could've slapped some claims about faulty tech, broken tech security, untrustworthy developers etc. on top of the rest.