That's actually a problem with marking, not with hand-counting. Machines are even less capable than humans are of inferring a voter's intent if the mark is ambiguous.

Touch-screens (or any one of numerous, less expensive machine alternatives) might be useful for ensuring that the voter doesn't vote an ambiguously marked ballot, but you don't need to replace real ballots with virtual ballot "images" to get the benefit. Just have the machine print out an unambiguous human-readable, voter-verifiable, machine-scannable ballot.

I also think the punch card concept could be improved upon to eliminate the chad problem while still having the advantages of a system that creates an unambigously marked ballot that is hard to alter or counterfeit.

Another advantage of physical ballots is that for cheating to go undetected by audits, every ballot that the cheater would want to have count differently would have to be handled in some way, compared to being able to secretly apply a formula to an electronic tabulation. (Is there a principle that describes intentionally building a system to be inherently inefficient as a way of slowing down attacks and accidental failures? Seems like there should be but I don't know what it is. I'd like to have a good retort for people who think electronic voting is wonderful because it's so "efficient".)

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