> If I had to guess, the complexity of counting may increase in a non-linear way after a certain number of precincts.
I'd bet that the larger counties, while they have more ballot counting machines, probably don't have proportionally more. Expensive, specialized, maintenance-intensive, etc. Every county needs at least one, but beyond that I doubt there is a huge priority on having excess capacity.
Ballot counting machines are probably a case of over-automation. The polls station clerks are volunteers and are maybe doing their first election. Setting up a manual process is just way easier then dealing with complex computer reporting systems. As soon as some machine or computer is not cooperating they are stuck. With pen and paper the worst that can happen is that the pen is out of ink.
I'd bet that the larger counties, while they have more ballot counting machines, probably don't have proportionally more. Expensive, specialized, maintenance-intensive, etc. Every county needs at least one, but beyond that I doubt there is a huge priority on having excess capacity.