Traditional paper ballot voting works wonderfully. It's reliable, hard to fake, and everyone can understand it. This means that people will have more faith in the system than some abstruse "blockchain" solution that nobody understands and demagogues can use to rabble rouse based on that lack of understanding. Those basic facts won't change just because there are other people influencing the election and some of the candidates are corrupt.
Also, borders would just change if people decided that they liked to be "borderless" with other entities; see the EU passport control etc. You'll still have local representation, districts, etc. As it turns out, maintaining law and order in meatspace is still a good thing and geographically grouped people is a magnificent way to regulate that.