There are digital records more than just a tally. Sure, maybe it's possible (with physical access) to destroyed or altered them, but the same holds for paper.
It's much harder to undetectably destroy or alter large numbers of paper records than it is to do the same to digital records.
It's also sometimes possible to do this to digital records without ever being physically present in their vicinity. Once again, this is much harder with paper.
It's very easy to forge paper records, though. I seem to recall reading about a rigged election in a questionable democracy where the ballot counters were given several file boxes full of fake ballots in addition to their local precinct ballots, with official anti-tampering seals intact.
It's also sometimes possible to do this to digital records without ever being physically present in their vicinity. Once again, this is much harder with paper.