>Provided you have a working democratic state with checks and auditing, what is the problem that voting machines solve?

It solves the problem of waiting days or weeks for a result. It solves the problem of multiple languages on a ballot. It solves the problem of visually-impaired voters accessing the voting machine, it solves the problem of incorrectly filled out voting sheets (hanging-chat).

Hell, that's just off the top of my head, and I'm sure others can contribute more.