The manual mistakes will average out with scale. Software mistakes get multiplied.

Nobody expects humans to be accurate, and that's why there are checks and balances in place to make sure the counts are accurate and unbiased. It would take a huge conspiracy to swing an election.

Computers represent a single point of failure, one piece of malicious software could affect an election and nobody would even know. This problem is made even worse by the closed source machines in use right now.

This is the key comment of this thread.

Assuming perfect security and absence of software bugs, we'd be insane to prefer human counters to machine counters.

Efficiency isn't always a good thing. Efficient systems can be more brittle, more centralized, and with errors that correlate. This is the story of inventing more and more efficient financial products until the whole system collapses due to interdependencies.

Sometimes you gain a lot by having deliberate inefficiencies.