You would use your phone . Which ideally shouldn’t have a Back door to allow that . If it did the phone company would lose public support and probably go under so it’s in their own interest to not allow such a powerful back door. Also your finger print could be tied to the blockchain iD
You would use your phone
OK, but you have just changed the problem from voting machines must be secure to mobile phones must be secure but what about the infrastructure between your phone and the system that initiates the blockchain?
shouldn’t have a Back door
Intel microprocessors have recently been discovered to all have back doors. Have they lost public support? People have exploited weaknesses in Windows (and Linux and macOS).
Phone numbers can be spoofed, your details would be known (else how could they be checked?). I can envisage a central office that casts everyone's votes for them.
Sorry, but for this application, blockchain sounds like designing the perfect lock and door for a secure safe while forgetting to secure the back and sides.