This, plus the inherent blessing and curse of computers -- if you can do something one time, it's usually very easy to do it 1000 times. If you want to tamper with one precinct or one county, you have to write some exploit. If you want to tamper with all of them, still, one exploit.
However, if you want to tamper with a whole state of paper ballots, you have to stuff a thousand ballot boxes. The chances of getting caught are far higher.
It's the same reason why voting via mail is very hard to exploit. Voting functions as a secure handshake (register to vote via mail, government sends confirmation, government sends ballot, you send ballot back, government sends confirmation of vote) and requires you to sign it with some identifying information like a signature.
There might be some individuals trying to cheat the system at the family level, but trying to cheat it at a larger scale requires you to do so at a point of collection. It also becomes very easy to find this sort of tampering by sending voters a way of confirming who they voted for.
One of the most egregious incidents of proven voting fraud in recent American history may have been by Leslie McCrae, a hired political operative: https://www.npr.org/2019/07/30/746800630/north-carolina-gop-... He exploited the absentee (mail-in) ballot system.
OTOH, he was caught precisely because to exploit the system he had to directly or indirectly expose himself to many people in the county--the people whose absentee ballots he was fraudulently collecting. Eventually someone put 2+2 together and the scheme was discovered.
OTOOH, apparently he had been doing it for many years before he got caught.
A more traditional voting system would have the same problem. He'd instead just put himself at a polling location and do the same trick there.
The fact that he had to pay people to collect individual absentee ballots means this sorta fraud is very hard to scale, easy to beat with some basic education and easily identifiable. Of course a lot of this goes out the window if you're doing it to help a party and that party has zero integrity but at least if one voting individual brings up an issue it can cause a ripple effect.
Part of the problem is also that we don't seem to take absentee ballots as serious as we do when we have full vote by mail.
I'm under the impression that computerized voting systems are in no way standardized nation-wide (USA, at least). But your point still stands that it seems easier to hack a computerized voting system to commit large-scale fraud than to fraud with paper ballots.
Yes this is true: federalism being applied to control of elections is probably good for election security. But there’s only a small handful of vendors and if an attacker was able to crack one of them they might be able scale the attack to many deployments of that vendor’s systems.
With paper ballots you must make sure that most people at the voting stations are part of the conspiracy, which is tricky because all major parties will have representatives on each station. It’s possible you will get away with it in a few small places, but even that is hard.
However, if you want to tamper with a whole state of paper ballots, you have to stuff a thousand ballot boxes. The chances of getting caught are far higher.