How would you ensure that someone can't vote for another person? How would you ensure that the person is alone when she votes?
So, despite all the flaws that you point out, why are these legal but a mobile app is not?
Here in Czech Republic we receive voting tickets by mail about a week before election and have to physically put them into a box behing a curtain in a voting room. I also see weakness here, and don't understand why we receive voting tickets by mail, because it allows you family relatives filter your tickets. Better system would be if the voting tickets were available only in the voting room.
Still it is better than web app. There are more security concerns with online voting, you can read more about it here: https://security.stackexchange.com/questions/15417/online-go...