> then why not just use the paper system?
One reason is efficiency, if you have the machines counting you get results faster and then you can audit only a random sample of machines records and get statistical guarantees of the election integrity. (The machine can't know before that it will be audited so if you test thousands of machines and find no discrepancy it's highly unlikely a significant portion of the others did cheat)
A second is that it allows one more level of trust. With a paper ballot you have to trust that the poll workers are going to notice/stop/not help ballot stuffing etc. In most cases that's a good enough guarantee, but with voting machines you can also trust the people who programmed audited it
If the poll workers are trustworthy, because of the paper trail, you don't have to trust the auditers of the machines, but if you don't trust the poll workers then you can gain a modicum of trust from the auditers
https://www.brookings.edu/blog/techtank/2019/12/06/how-elect...
This link talks about the benefits in the indian election, specifically a software lock on the amount of votes per minute that can be cast
It also shows that in 2013 they audited "only" 20k machines out of almost millions yet found no discrepancy. Statistically that's probably good enough if the choice of machines audited was random
One last way it might be useful, though this is an abstract scenario, is if you want to deploy a more complicated to count voting system to large areas. In some voting systems counting can't be done in parallel, you need to do one round of counting, wait for everyone else and then do a second round and so on.
Similarly some voting systems might benefit from a digitized interface (for instance ballots in austria look like this: https://cdn1.vienna.at/2013/09/zettel.jpg and there are systems which would lead to even larger forms) which outputs a paper trail with only the actual information the voter inputed (in the case of the ballot I showed it'd pretty much just show a party name and a list of candidate names)
In these cases a machine outputting an auditable digital model of the votes cast would greatly simplify counting procedures. You could have every polling station just publish a signed file with the votes in their station and everyone could run the election algorithm
The votes can then be audited same as in the indian system