There isn’t that much money to be gained. I work for a Danish muniplacity and we do digital voter registration, but I don’t think we’ll ever do digital voting because it’s unsafe.
Our system is a little different, here every citizen is mailed a “ticket” they can exchange for the voting ballot in the weeks leading up to the election. If yours is lost in the mail, no worry, we can print you a new one, and you can’t really use someone else’s because it has your name on it and we check.
In every ticket there is a barcode that we scan, to speed handing the out ballots up, this also counts the amount of voters, and that’s the digital part of the election. It’s also the most burdensome, so this is where digitisation saves us time.
The voting is done on paper and counted in hand, and checked with the amounts who have passed through the digital system, if it’s off by more than 1-3 votes there is a recount until it fits.
The counting takes a few hours at each location, but it’s done by the same people who’ve worked the voting place all day to ensure the safety of democracy, so it’s not really that expensive or inefficient.
And that’s not accounting for the cost of voting machines. The digital part of our elections is the most expensive part of the process, because digital systems are expensive.
We use them because they add convenience for the citizens since they eliminate queues, but it would actually be much cheaper to do the whole process on paper.
I’m not sure why America ever installed digital voting machines, but I can’t see any reason to do so. Especially not some that don’t leave a paper trail.