What problem do electronic voting machines actually solve? The US didn't seem to have problems counting millions of paper ballots (save for some hanging chads) until the "solution" of electronic voting machines appeared.
1. Allowing people with disabilities to vote. For example, headphone voice prompts for blind people, large print/high contrast for the elderly etc.
2. Making sure voters understand the voting procedure - particularly if there are multiple offices and issues on the ballot, multiple ballot papers and so on.
3. Ensuring voters' intent is recorded unambiguously. For example, you can't put marks in multiple boxes (intentionally or accidentally) and you can't leave a dimpled or hanging chad.
4. Perfect counting (assuming the data is entered correctly and the software works right) as opposed to manual counts where papers sometimes end up in the wrong pile.
5. You can offer voting in multiple languages.
6. You can randomise the order of candidates on the ballot, to evenly distribute any impact being at the top might have.
7. Ability to take backups for transit or deliver results electronically, avoiding boxes of ballots going missing.
8. Reduced counting costs and faster results, allowing more polling stations to be operated and allowing the polls to stay open later for the same result delivery deadline.
Whether it succeeds at offering these benefits, and whether they're worth the obvious cost in trust is debatable.