I'm not sure then what urgent problem you're trying to solve that warrants the cost of errors introduced by the manual counting of huge amounts of paper ballots. It would also be a logistical nightmare getting reams of paper to voters and getting them back and tracking them; at my polling place, we have to make sure that the number of ballots we issued out equals the number reported by the scanner (plus the number of spoiled ballots voters returned to us for disposal). I'm just pointing out that cost.
If you don't trust the tabulating machines, we have mechanisms to check them at scale. Basically, randomly sample the paper ballots and check them against the machine results. https://en.wikipedia.org/wiki/Risk-limiting_audit
If you don't trust the people running elections, you should know that polling places in the US are run by community volunteers. Literally anyone who's a registered voter can participate and see how the sausage is made. In fact, there's a shortage of these folks, so boards of election are thrilled to get more people participating.