I agree with that to a degree. The problem is we are trading off technical problems for corruption. For counting things, it seems like computers would be a good fit.
You could keep the computers but you also have the papers sealed in boxes. Then you can manually check 1-5% of the votes and make sure the machines are correct. Or if someone contests the count and a judge decides the reasons are fair you can count again all the votes in that polling station.
UNIVAC famously analyzed the 1952 presidential election. Today we've got about twice as many voters, so maybe get a computer twice as powerful as a UNIVAC.