> Paper ballots counted by hand can and can achieve all the things we desire in election systems.
Sometimes, it's about efficiency as well. I've been a ballot worker here in Germany for the 14 years since I was eligible.
There are simple elections: electing a mayor, for example. You have a ton of DIN A4 paper sheets, but you simply sort them into heaps, count the heaps, and you're done. These don't really benefit from computerizing them, other than speed, but even for a larger polling station, you're done in an hour or two.
Then there are more complex elections, like the German Bundestag, where you have two votes on one DIN A4 sheet: the "Erststimme", where you vote for the directly elected representative of your district, is just as easy to count as the mayoral elections. But then you have to go through all the ballot papers again to count the "Zweitstimme", where you vote for the party lists that make up the other half of the Bundestag. While most people vote the same in both where you can short circuit during the first phase of sorting, IME around half the people vote different (say, they vote for the SPD candidate in primary because he's the one that will most likely have success over the CDU conservative, but in secondary vote they vote Greens or Left), so it's still a sizable amount of paper you have to touch twice.
And then there are the horrors: the European Parliament election [1] or regional/city elections [2], where each ballot paper can reach almost 1 m² in size making them very difficult to handle, and you have a ton of ways to distribute your votes across parties ("Panachage" [3] and others), so for the (again) about half of people actually using the complex distribution you have to painstakingly check and count votes. Having these computerized would eliminate so much trouble, particularly as there's always 5-10% of voters who mess up their maths, rendering sections or their entire vote void. And counting these can last for days of very mentally intensive work.
On top of that come specialized voting schemes such as ranked choice and its countless variants, where some are very difficult to execute without having a computer that can run through vote combinations as a batch job.
[1] https://www.pnp.de/archiv/1/europawahl-altoettinger-druckere...
[2] https://www.sueddeutsche.de/muenchen/kommunalwahl-muenchen-w...
[3] https://en.wikipedia.org/wiki/Panachage
[4] https://en.wikipedia.org/wiki/Ranked_voting